If you have purchased uninsured motorist property damage coverage you can claim the damage to your vehicle through that part of your policy. If you only have liability and the at-fault person does not have insurance you will most likely have to go after them personally to get your vehicle repaired.If the person received a citation for driving without insurance their penalty for that, in Georgia, should be a 60 to 90 day suspension of their license plus fines and conditions.

Hopefully you had the police come to the scene and make out a police report showing that the blame is with the other person for the incident. If so you might want to take this and request they pay your damages. If they do not want to pay, you will likely have to take them to court or at the least get legal advice about your situation.