Thinking about applying for citizenship, but have a DUI (driving under the influence) or DWI (driving while intoxicated) on your record? In many states it is still possible to become a U.S. citizen even though you have had one (or sometimes two) convictions for drunk driving in your past.n addition, people with a DUI or DWI may wish to hire an Immigration Attorney to go with them to the citizenship interview, as the interviewing Officer will be asking many intense questions about good moral character in general for the previous five years because of the drunk driving conviction.