According to the Georgia Dental Hygienist Association, to get your license, you'll need to verify that you are a Citizen or legally present in the U.S. You can use your EAD Card for this.
Georgia Dental Hygienist Association
Other than that, to get an Associates of Science in Dental Hygiene is to do the courses at a college/university/trade school. Every college is different when deciding whether to allow you in-state or out-of-state tuition.