Depends on the state. Virtually impossible in Calkfornia, requiring a governor's pardon, which is ponderous to seek and rarely granted.

State's have legal mechanisms to get your civil rights restored. Generally, this requires petitioning the sentencing judge to restore your civil rights, and may require specifically asking for the right to possess a firearm. There may be other requirements besides just asking, you should consult a lawyer in the state you live.