Texas law says no, but it contains an exception. Section 46.04 of the Texas Penal Code makes it illegal for someone convicted of a felony to possess a firearm.The law does not allow felons to possess firearms at any other location. To be eligible for a pardon in the State of Texas, you must be fully discharged from the felony, misdemeanor, or traffic offense sentence you received. You have to petition the court system that took your civil rights away to have them reinstated. Of course it is up to a judge. Under Texas law, a convicted felon cannot possess a firearm. Possession of a firearm can have significant legal consequences for felons. Section 922(g) is the law that prohibits felons, and certain other groups, from possessing firearms. While these laws have proven effective in other states, Texas lawmakers have not pursued them, citing concerns over Second Amendment rights and due process.