This is not a criminal defense / dwi question. It is an immigration law question. That being said, a misdemeanor offense is USUALLY not enough to require removal. This assumes that the offense in question was a misdemeanor and not a felony. That being said, because a DUI in Alabama carries a POSSIBLE penalty of 1 year in jail, the analysis needs to be expanded. There is an apparent consensus that DUI is not a crime involving moral turpitude. This has not (to the best of my recollection) been finally decided. Thus, if an immigration judge found that DUI is a crime involving moral turpitude and it is punishable you one year in jail, the conviction could affect admissibility status.
To be on the safe side, I recommend consulting with an immigration attorney as soon as possible.
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I definitely suggest consulting with an immigration attorney. While you conviction probably won't result in deportation, hiring an immigration attorney will make the process much smoother. Good luck.