The short answer: If you are a resident of the State of Georgia for at least 6 months, you can file for a divorce in Georgia. The status of your citizenship is between you and the INS. Hope this helps and Good Luck!
I see the answer that was posted, but I think your question is more concerned with whether a divorce will impact your citizenship application. While you can get divorced, it may indeed have adverse impact on your application. You will want to address this question to an immigration attorney before taking any action.
As long as you have resided in the state for 6 months, you can file for divorce.
While I can answer the divorce end of things I am not an immigration lawyer, and you should ask one to see what effect it may have on that.