It is legal to own and possess a serval in Georgia provided you have the requisite licence or permit. Conversely, it is unlawful to import, transport, transfer, sell, purchase or possess a serval in Georgia without first obtaining a wild animal licence from the Georgia Department of Natural Resources (believed because the department is not stated in the law that I have seen). In fact, this rule applies to all animals in the taxonomic order called Carnivora except for the European ferret. That means it applies to all wild cat species.
I have been able to read the exact law on this subject so I can vouch that this information is accurate as at 2020 (the law changes sometimes). You can click on this link to read it yourself if you wish (but please be aware that sometimes over time links to outside websites break). This is a Georgia wildlife provision enacted in the public interest to ensure the health, safety and welfare of the citizens of Georgia.
You will have to do contact the relevant department which I believe to be the one mentioned above. I have been unable to find an example of the terms and conditions of these licences so I’m afraid you’ll have to contact the department yourself and go through it. I’m sorry for that but sometimes the Internet does not provide this sort of information or if it does it is very hard to find. I’d expect the terms of the license to be quite restrictive.
Postscript: if you’ve never interacted with a serval before I would advise that you meet one in their enclosure and interact with the cat to see what you think. The males are quite big and they can be intimidating. They do not act like domestic cats even when tame, which is to be expected. They have to be confined to the home which provokes them to escape as their natural range is around 10 square kilometers. They often escape and are sometimes shot once they are in public areas. They sometimes spray urine inside the home to mark territory (in the wild they can sometimes spray 95 times per hour!). They are quite a handful and if you can get over all these issues you must never declaw a wild cat of any kind. A serval’s claws are quite large, similar to the claws of a large dog. Some people declaw their ‘pet’ servals which compounds the whole incorrectness of the process in my view.