In Georgia, expungement is the only legal method to completely remove an arrest from a criminal record. There are very few instances that qualify to have an arrest removed from your criminal history. Generally speaking, it is used only for arrests where charges are later dropped. Expungement is not used to remove convictions, nor is it used to remove charges that later lead to trials where the defendant is acquitted.
While there is no way to have this conviction "Expunged" from your record you might want to look into a pardon from the Georgia Board of Pardons and Paroles. This would not remove the conviction from your record but would restore whatever rights you have lost, if any, due to the conviction.