Can I get my boyfriend his green card if we get married outside of the US?

Getting married in Mexico is fine and would be recognized for immigration purposes; alternatively you can petition for him to come as a fianc and file documents for his permanent residency in the U.S. We would need to evaluate the complete immigration and criminal history of your boyfriend to determine whether there will be any problems getting him back? Was he here in status? Did he enter illegally? Did he overstay his visa? Has he ever returned to the U.S. after accumulating out of status time and then leaving? Details of his DUI are needed. Does he have any other arrests or convictions? He will need to show that he is not dependent on alcohol. When did the DUI occur? I would suggest a consultation to go over all of these questions with him on the phone and with you either on the phone or in person. This can be arranged by calling my office and scheduling and arranging payment.

In general, if someone enters the U.S. unlawfully and without inspection, he may not adjust status in the U.S. to become a Lawful Permanent Resident (to get a "Green Card") even if he becomes married to a U.S. citizen. Additionally, if as an adult he is unlawfully present in the U.S. for a year or longer, he may become subject to a very harsh 10-year bar to re-entering the U.S. Applying for him as a fianc may be possible, and applying for him as your spouse following a marriage in Mexico may be possible, but it would be wise to engage an immigration attorney to carefully review all details and circumstances relating to immigration eligibility before making an decisions. That would include carefully reviewing the dates he already may have been unlawfully present in the U.S.