No you don't need a visa.
You can enter for 90 calendar days in any 180-day period on either your Schengen or USA visa.
Aliens holding a visa and/or a residence permit of any country listed above may enter and stay in Georgia without visa for 90
calendar days in any 180-day period.
For the purpose of entering and staying in Georgia without visa, a visa and/or a residence permit of a respective country shall be valid
on the day of entry into Georgia (crossing the border), which must be
evidenced by a travel and/or other appropriate document.