A single DUI should not affect your Citizenship application.
I would still recommend having an attorney review your documents (conviction) to ensure that there you are eligible.
USCIS will not approve an application for citizenship while someone is on probation.
(c) Proof of good moral character in certain cases
(1) Effect of probation or parole. An applicant who has been on probation, parole, or suspended sentence during all or part of the statutory period is not thereby precluded from establishing good moral character, but such probation, parole, or suspended sentence may be considered by the Service in determining good moral character. An application will not be approved until after the probation, parole, or suspended sentence has been completed.
8 CFR 316.10(c).