In Texas, a convicted felon can get his/her rights to possess a firearm after 5 years. Here is the statute:
Texas Penal Code 46.04
§ 46.04. UNLAWFUL POSSESSION OF FIREARM.
(a) A person who has been convicted of a felony commits an offense if he
possesses a firearm:
(1) after conviction and before the fifth anniversary of the person's release from confinement following conviction of the felony or the person's release from supervision under community supervision, parole, or mandatory supervision, whichever date is
(2) after the period described by Subdivision (1), at any location other than the premises at which the person lives.
(b) A person who has been convicted of an offense under Section 22.01, punishable as a Class A misdemeanor and involving a member of the person's family or household, commits an offense if the person possesses a firearm before the fifth anniversary of the later of:
(1) the date of the person's release from confinement following conviction of the misdemeanor; or
(2) the date of the person's release from community supervision following conviction of the misdemeanor.
(c) A person, other than a peace officer, as defined by Section 1.07, actively engaged in employment as a sworn, full-time paid employee of a state agency or political subdivision, who is subject to an order issued under Section 6.504 or Chapter 85, Family Code, under Article 17.292 or Chapter 7A, Code of Criminal Procedure, or by another jurisdiction as provided by Chapter 88, Family Code, commits an offense if the person possesses a firearm after receiving notice of the order and before expiration of the order.
(d) In this section, "family," "household," and "member of a household" have the meanings assigned by Chapter 71, Family Code.
(e) An offense under Subsection (a) is a felony of the third degree. An offense under Subsection (b) or (c) is a Class A misdemeanor.