How do you get an id card as a felon?

Highly unlikely. If the DMV is the agency for issuing the "Officiial" state ID card, you will have to produce valid, legal proof of your identity (birth certificate - passport - etc) and they are going to run your name and DOB through the computer system. Guess what they're going to find?

My friend in GA had a bench warrant for FTA and she renewed her learner's permit twice, took the driving test, and ultimately got her driver's license without it coming up.