US layover Petty Offense Exception for passenger with a criminal record

tl;dr: you can't apply for "petty offense exception". If you were summary convicted then just go ahead. If you were indicted then you have a problem and need to fill an I-192, it's a lengthy process. Both are possible for theft under $5,000, we do not know which one happened to you.

Let's get legal, shall we? You won't find "petty offense exception" at any official site because that's just a nickname. section 212 of the Immigration and Nationality Act has this:

(i) In general.-Except as provided in clause (ii), any alien convicted of, or who admits having committed, or who admits committing acts which constitute the essential elements of-

(I) a crime involving moral turpitude (other than a purely political offense) or an attempt or conspiracy to commit such a crime, or

(ii) Exception.-Clause (i)(I) shall not apply to an alien who committed only one crime if-

(I) [not relevant to you] or

(II) the maximum penalty possible for the crime of which the alien was convicted (or which the alien admits having committed or of which the acts that the alien admits having committed constituted the essential elements) did not exceed imprisonment for one year and, if the alien was convicted of such crime, the alien was not sentenced to a term of imprisonment in excess of 6 months (regardless of the extent to which the sentence was ultimately executed).

If the maximum prison term for your offence is less than a year and also you were not sentenced for more than six months then just go ahead. The infamous "inadmissible for moral turpitude crime" simply does not apply in your case.

Now the Criminal Code of Canada » 334. Punishment for theft

of an indictable offence and is liable to imprisonment for a term not exceeding two years, or

of an offence punishable on summary conviction,

where the value of what is stolen does not exceed five thousand dollars.

The Crown decides how they prosecute. If it was a summary conviction then your maximum sentence was six months (that's what summary conviction means) and then you are good to go the USA. If they decided it was an indictable offence then you are out of luck since the maximum sentence is two years.