Traveling to US with ESTA but have an Iranian father. Do I need a visa instead?

On Visa Waiver Program Improvement and Terrorist Travel Prevention Act Frequently Asked Questions, the U.S. authorities state:

How is “dual citizen” or “dual national” defined? What if I was born in a country, but never lived there and do not consider myself a national or citizen?

We will make nationality determinations in accordance with U.S. legal standards and practices, not merely by reference to the laws and practices of foreign governments.

which is really clear as mud, because it does not shed any light on how "U.S. legal standards and practices" determine that, and in which situations the result of "U.S. legal standards and practices" could possibly differ from "laws and practices of foreign governments" that do consider all male-line descendants of of their citizens unto the n-th generation to belong to them forever.

One almost gets the impression that this confusing signaling is deliberate ... the new rules seem to have been the subject of considerable controversy within the U.S. and it may be that the CBP are trying to give non-answers that they think are most likely to mollify critics from both sides, while being vague enough to let them do whatever the heck they want to do in practice.

As a pragmatic matter you should probably resign to needing a visa. The consequences of making the wrong call in the other direction are too great (at least for most people's risk tolerance), and it doesn't seem likely that you're going to get an authoritative answer from anyone in charge that unambiguously says that people in your situation are not covered by the rules.

This is the full answer about "dual national" from the VWP Improvement FAQ cited by another answer:

How is “dual citizen” or “dual national” defined? What if I was born in a country, but never lived there and do not consider myself a national or citizen?

We will make nationality determinations in accordance with U.S. legal standards and practices, not merely by reference to the laws and practices of foreign governments. If an individual believes that he or she is eligible for an ESTA travel authorization, the individual should apply for an ESTA, answer all questions truthfully and accurately, and that individual’s eligibility for an ESTA authorization will be determined in accordance with U.S. law. If you have any questions, please contact CBP at 1-202-344-3710.

I agree that "in accordance with U.S. legal standards and practices" is not very specific, but we aren't entirely in the dark since it is U.S. legal standards and practices that also determine U.S. citizenship practices.

I've modified from the original to make the argument less contentious, though I believe it is the same argument. Under US law citizenship is voluntary and there is a fundamental right to expatriation if you might have it but don't want it. The original expatriation law (R.S. §?1999) was passed in 1868 at the same time automatic jus soli citizenship was added to the constitution, and says this:

Whereas the right of expatriation is a natural and inherent right of all people, indispensable to the enjoyment of the rights of life, liberty, and the pursuit of happiness; [...] Therefore any declaration, instruction, opinion, order, or decision of any officer of the United States which denies, restricts, impairs, or questions the right of expatriation, is declared inconsistent with the fundamental principles of the Republic.

What this means, as is made clearer by the context in which it was enacted, is that even if you have an automatic obligation of or right to citizenship (anywhere) you are free not to accept it or to abandon it, and be treated consistent with that choice under US law. What your past nationalities might have been aren't relevant. Current law (8 USC 1481), to which the above is attached as a note, allows US nationality to be shed by the mere intention to do so coupled with a foreign naturalization or formal oath of allegiance (i.e. there's an inhibition against abandonment to statelessness) if you are an adult (i.e. your parents can't make an irrevocable decision for you).

Given this, my best guess is that the US would never consider someone who is a national of somewhere other than Iran, who claims no Iranian nationality and who has taken no action (travel, obtain documents, join the army) that would suggest otherwise, to be an Iranian national no matter what the parents' nationalities were and no matter what Iranian law says. It also isn't a coincidence that the ESTA nationality question is present tense, to be consistent with the law above. If they were interested in possible past connections with Iran they'd also ask about places one has lived and/or the birth places of the parents, but since they didn't ask that there's no reason to answer that. That's all just a guess, though.

I hence think the best answer is that the OP should call 1-202-344-3710, explain his situation and ask them what they think.

P.S. So I phoned that number myself and presented the person that answered with the following entirely-made-up facts about a person:

• Born in Hong Kong, has Hong Kong and UK nationality
• Has a valid ESTA listing those nationalities
• Father is an Iranian national
• Birth not registered with Iran
• Has relatives in Iran, but has never been there

I then asked if the person now required a visa. The lady I was talking to asked two things:

• Where was the person born? I said Hong Kong.
• Has the person ever had an Iranian passport? I said no.

The lady then said that no visa was required and the person could travel on her existing ESTA.

The actual facts for the OP might not be those but I assume if they are similar the answer will be the same if she phones (she may also talk to the same person, as the call sounded a whole lot more like a not-very-busy phone on someone's desk than it did a call centre operation). This clearly doesn't preclude applying for a visa instead, but I think doing so for no purpose other than being able to mention the Iranian father because the ESTA application didn't ask about that might be committing a TMI error.

You can find the Iranian nationality laws in 'The Civil Code of the Islamic Republic of Iran' article 976 ff. Basically, all children of Iranian men are considered Iranian citizens (article 976.2), also if they were born outside Iran and have never lived there. Since it is up to the 'issuing' country to define who are considered their citizens, I don't really understand your question if the US would consider you a Iranian citizen or not. That is not up to the US government to decide.

Being an Iranian citizen unfortunately now excludes you from travel to the US under the Visa Waiver Program:

Citizens or nationals of the following countries (..., United Kingdom, ...) are currently eligible to travel to the United States under the VWP, unless citizens of one of these countries are also a national of Iraq, Iran, Syria, or Sudan.

Having a valid ESTA is just another additional requirement to travel under the VWP. Since your citizenship makes you ineligible for travel under the VWP, it is irrelevant if you have a previous unrevoked ESTA.

Edit: You can of course, as suggested by Michael Hampton in his comment to your question, try to enter with your British passport and deny your Iranian citizenship. If you are lucky, US immigration won't notice and let you in. If they notice, you will be denied entry and receive an entry ban for the foreseeable future for having used deception trying to gain entry to the US.

Edit: Just to backup my comment, in which I state that citizens are always considered nationals as well, here a quote from the definition of 'allegiance' in the 'The Law Dicitionary':

The citizen ... owes an absolute and permanent allegiance to his government or sovereign, ...

First of all, never lie to immigration. This has been repeated very often on this site. What Tor-Einar Jarnbjo's otherwise correct answer is missing is he considers "national" and "citizen" the same and it is most definitely not! For example, people born on American Samoa are USA nationals but not USA citizens.

So, what is a national? Let's read the law:

(21) The term “national” means a person owing permanent allegiance to a state.

Well, do you owe permanent allegiance to Iran? Disclaimer: I am not a lawyer. I am just pointing out the law. You can read it, you can interpret it on your own.