If you can show he actually entered the U.S. legally and you are a U.S. Citizen, he will be eligible to adjust in the U.S. (assuming he does not have a deportation order). Please see more below.
Brian D. Lerner
Attorney at Law
I agree with the previous attorney respose. If he can prove he entered with a visa, and you are a U.S. citizen, it is possible he can file for his green card based on your marriage. He should try to get the original visa he used to enter and then I would recommend you have a consultation with an reputable immigration attorney to review all of the details of the case. Being married to a U.S. citizen does not guarantee him a green card and so it is important to review his complete immigration and criminal history with an attorney before you start presenting his applications with immigration. Just having a consultation with an attorney does not obligate you to hire that attorney to prepare the case. But at least you will have a professional evaluation of the case to know how to move forward.