Can I reapply for an ESTA if I've been previously deported/removed from the US?

Once you have been found to have broken the conditions of a VWP visit once, you are forever excluded from the Visa Waiver Program, and will only be able to enter the US again by getting a visa in advance (or becoming a Canadian citizen). This holds even if you manage to get an ESTA approved, because "no prior violations" is a condition for entry in addition to having an ESTA. (8 U.S.C. 1187(a)(7)).

(In contrast, merely having a visa refused in the past, which is also generally a barrier for using the VWP, stops being relevant if one actually gets an ESTA).

Furthermore, since you were removed from the US at some time after 2011, this removal comes with an automatic 5-year entry ban under 8 U.S.C. 1182(a)(9)(A)(i). You can apply to have the ban lifted using Form I-212 (which will set you back $930 just for the asking), and this is in addition to applying for a visa. It appears that you can ask to have the ban lifted as part of a nonimmigrant visa application -- ask for details about this at the consulate you apply to.

(It is possible that you were not actually formally removed when you were refused entry, but were instead allowed to withdraw your application for entry and leave voluntarily. This difference would probably not have seemed important to you at the time, but it controls whether you now have a ban or not. Have you held on to any paperwork you got at the time?)

According to the US Customs and Border Protection website, your ESTA application is unlikely to be successful if you were "previously denied a visa, or previously refused entry to the United States, or previously removed from the U.S."

https://help.cbp.gov/app/answers/detail/a_id/1097/~/previously-denied-a-visa-or-immigration-benefit

You can apply, but are unlikely to be approved.

From the CBP Website:

Q: Should a traveler not approved for travel through ESTA reapply?

A: Unless the circumstances have changed, the traveler will not qualify for an ESTA and will need to apply for a nonimmigrant visa at a U.S. Embassy or Consulate. If you misunderstood the question, or thought something in your background was a reason to be denied and found out later that it was not, we advise you to contact us so we can review your answer. Please go to help.cbp.gov to send an email by clicking on “Ask a Question.” In your email, please explain why you selected "yes" to that question, and ask for clarification on next steps.

So, while technically not for cases like this, you definitely can contact the CBP through their contact form and ask, but you then have to prepare to attach as much proof as you can (you can upload files in the contact form), including official proof of your business, your University degree, your property contract, marriage/birth certificates of any spouse/children you may have, other proof of family and friends...any proof of ties to Argentina strengthening the belief that you will return home.

In addition, attach an explanation letter from your cousin stating why he gave you money, along with documentation proving that it was only for recreational purposes, and that you did not take up employment with a US employer.

It's not very likely it will change anything, but honestly, you have nothing to lose by trying.

Of course, if all else fails, a B-2 visa is the way to go. The good news is they're multiple-entry and valid for 10 years, with the holder usually being granted a 6-month leave on each entry. In addition, if you were refused an entry ban, you can ask to have that ban lifted as part of the visa application.

The bad news is they cost USD 160 and you'll be much more scrutinised, and having been refused entry isn't going to look pretty to the visa officials. If you end up having to pursue this route, bring all forms of documentation I mentioned above, to show them just in case.