Georgia can take a long time. The GA DOR website says often 90 business days or more (i.e., 4 months). Several states are taking a long time as they crack down on detecting fraudulent returns. But there are a couple of things you need to do.
You need to first check to be sure that your return was successfully filed.
If you efiled, what do you see when you check with this tool? Was your state return accepted?
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
If that showed your efiled state return was accepted, or if you printed and mailed the return, the FAQ below tells how to check on a state refund.
FAQ: How do I track my Georgia state refund?
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-georgia-tax-refund/00/26560
