It's not uncommon for someone to make a one-time mistake, get into a car after having one drink too many, and end up with a conviction for drunk driving--or in legal terminology, a DUI or DWI. Is this going to present any problem for their U.S. visa application?
By itself, a single DUI does not automatically make a foreign-born person inadmissible to the United States. (See Crimes That Make U.S. Visa or Green Card Applicants Inadmissible and the grounds of inadmissibility in Section 212(a) of the Immigration and Nationality Act (I.N.A.).)
But that's not necessarily the only consideration, as described next.
Every applicant for an immigrant visa to the United States (lawful permanent residence or a green card) must get past the official medical exam with a civil surgeon (a doctor) in their country. And one of the things the doctor will be looking at is whether the applicant might be an alcohol abuser.
As stated in a State Department set of guidelines called the Foreign Affairs Manual, at 9 FAM 302.2-7(B)(3)(U), a diagnosis of having a substance-related disorder does not by itself make an applicant ineligible for a U.S. visa, "unless there is evidence of current or past harmful behavior associated with the disorder that has posed or is likely to pose a threat to the property, safety, or welfare of the applicant or others in the future." A DUI or DWI could supply that evidence of harmful behavior.
Also, even if you're applying only for a nonimmigrant, temporary visa to visit the United States, it's entirely likely that the U.S. consulate in your home country will, upon seeing the drunk driving conviction on your record, refer you to a civil surgeon for evaluation before making a decision on your visa application. The FAM directs them to do so in cases where there has been:
What happens after that is largely up to the judgment and expertise of the civil surgeon. You will not be allowed to see the report that the doctor prepares concerning you. If you are found inadmissible, however, you may apply for a waiver with which to enter the United States.
Fully evaluating whether you are inadmissible and, if warranted, preparing a waiver request is best done with the help of a U.S. immigration attorney.