Can an ex-felon (non-aggravated or non-violent in nature) become a legal RESIDENT if married to a US citizen?

He hasn't been in trouble for over 7 years at this point, has lived here almost since birth, and is a stable/good man. He was given 6 months jail for stealing gift cards from his job when he was a teen. But because we live in Texas, we aren't able to have the record expunged- perhaps set aside, but I doubt that would help where it concerns immigration. He doesn't want to even try to become a U.S. Citizen anymore after all the money he's wasted on scam lawyers- we just want to apply for residency so he doesn't have to worry about being deported to a country where he will be homeless and have no family. He can't even speak spanish properly. lol