From the Georgia Office of Bar Admissions website:
In order to sit for the Georgia Bar Examination, you must submit a Bar Examination Application to the Board of Bar Examiners. All Bar Examination Applications must be submitted online and the appropriate filing fees must be received in the Office of Bar Admissions before 4:00 p.m. on the posted Bar Examination Application Filing Deadline. ALL POSTED TIMES ARE EASTERN TIME. U.S. Postal Service postmarking by the posted deadline IS NOT accepted as timely receipt. In order to apply for the Bar Examination you must first log in to the Office of Bar Admissions website at www.gabaradmissions.org. If you have not previously done so, you should click on the Register link at the top of the page and provide the requested information. You should log in to your User Home Page, click on Application Forms tab, then click on Apply under the Bar Exam Application heading. You should answer the six (6) Exam Eligibility questions and click Submit. Your eligibility request will be forwarded to the Office of Bar Admissions. Within 2 business days, a staff member will review your request and you will receive an email with instructions on how to complete the Bar Examination Application process and pay the appropriate filing fee. Keep in mind that you WILL NOT be considered registered for the Bar Exam until you complete all of the steps outlined in the instructions that will be emailed to you.
You can still file that application between June 2 and July 1 but you will pay a large late filing fee. Remember, this is separate from and in addition to your application to be certified through the Character and Fitness process. When you received that certification, you should have gotten instructions about the next step, to apply to take the actual examination, which is described above.