Unfortunately, Immigration has every right to deport you. However, on the other side of the coin, you do qualify for a Waiver (assuming the sentence was less than 1 year.) Thus, it would be critically important that you apply for the proper forms of reliefs and waivers to try to win the removal/deportation proceedings. Depending on how long you have been here and when you got your Green-Card, you may also qualify for Cancellation of Removal for Lawful Permanent Residents.
Brian D. Lerner
Attorney at Law