No, you can't just "make" her leave. You need to begin the process of eviction (known as a dispossessory in Georgia). You begin by providing her a Pay or Quit notice giving her a certain number of day to pay her rent (I give my tenants 3 days) or "quit"...leave. If she does neither, you then go down to the Clerk of Court's office in your county and begin the process of evicting her.
Do a "google" search on evicting someone in your county of Georgia. Most counties will provide you information on how you go about doing this and what you must provide to the court.
Often the Pay or Quit notice gets deadbeat tenants moving one way or the other.
Gail