Having a felony conviction usually revokes your ability to have, possess, or otherwise control a firearm. There are, however, avenues that can be taken to petition the court to have this right restored.
You will want to contact an attorney who does criminal work about this situation.
Arizona law allows for the restoration of firearm rights for most convictions two years after probation is completed or the date of absolute discharge from imprisonment. If you were convicted of a serious offense or what would be a "serious offense" under 13-604, you can have your Second Amendment rights restored 10 years after you have been discharged from probation or released from prison.
If your offense was considered a "dangerous offense" under section 13-604 (This usually means a felony conviction involving the intentional or knowing infliction of serious physical injury or the use or exhibition of a deadly weapon or dangerous instrument), Second Amendment rights cannot be restored. Restoration of firearm rights will allow a person to own, possess or use a firearm as long as they are not restricted according to the federal domestic violence ban.
The typical case in Arizona takes about 3 to 4 months. The courts operate on a first-come, first served basis, so the sooner you start, the sooner your conviction is set-aside.
There is a lifetime prohibition from the United States government, which prohibits firearm ownership of those convicted of misdemeanor domestic violence as defined by federal law. The federal definition is different than Arizona’s definition