Yes, Georgia does have a helmet law which requires all riders on a motorcycle to wear a helmet.
This "helmet law" is listed under Title 40 of the GA Code under the Motor Vehicles and Traffic laws, Chapter 6. Uniform Rules of the Road. Article 13. Special Provisions for Certain Vehicles. Part 2. Motorcycles. Section 40-6-315 is titled Headgear and eye-protective devices for riders. Here it states:
(a) No person shall operate or ride upon a motorcycle unless he or she is wearing protective headgear which complies with standards established by the commissioner of public safety.
(b) No person shall operate or ride upon a motorcycle if the motorcycle is not equipped with a windshield unless he or she is wearing an eye-protective device of a type approved by the commissioner of public safety.
(c) This Code section shall not apply to persons riding within an enclosed cab or motorized cart. This Code section shall not apply to a person operating a three-wheeled motorcycle used only for agricultural purposes.
(d) The commissioner of public safety is authorized to approve or disapprove protective headgear and eye-protective devices required in this Code section and to issue and enforce regulations establishing standards and specifications for the approval thereof. The commissioner shall publish lists of all protective headgear and eye-protective devices by name and type which have been approved.
Riding a motorcycle without a helmet in Georgia is a misdemeanor which can come with a fine of up $1000 and/or 12 months imprisonment.