This is a question better posed to an immigration attorney. However, it is my understanding that a simple first time DUI offense is not a deportable offense. You should neverthelss consult with an immigration attorney to confirm this.
A DUI can pose a problem for naturalization since many immigration offices consider it a sign of a lack of good moral character. As far as permanent residency is concerned, if it was an isolated, single incident and there were no injuries, then it will probably not prohibit the issuance of the green card.
So long as this is a simple first offense, the only thing you'll find is that you cannot apply for citizenship until you've completed probation. It is better to fight your DUI case and attempt to keep it off your record.
Good luck on your case.
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