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You would need to first apply for and be granted a full pardon. Assuming you are granted a full pardon (and pardons are very rarely granted), you could then file for restoration of firearm rights. Even then, just so you know, the Board of Pardons and Parole will generally only consider restoring gun rights to an individual where they require a gun for their livelihood, and the inability to own a weapon is interfering with that.
Thus, it is a long shot, and it's not a quick process by any means, but that is the process you would have to go through.
If you would like any additional information or have more questions please don’t hesitate to ask!