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. Under Texas law, individuals convicted of certain felonies are prohibited from possessing firearms. 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. Simply put, former felons cannot possess guns in their cars or on their persons (other than inside their own homes) in the State of Texas. Under Texas law, a convicted felon cannot possess a firearm. Possession of a firearm can have significant legal consequences for felons. Federal Law Restrictions: Under federal law, individuals convicted of a felony are prohibited from possessing firearms. Just having the firearm in a convicted felon's possession is breaking the law.