From traveldoc.aero
Visa is required for passengers holding travel documents issued to
stateless persons, refugees or aliens.
However, you can apply for eVisa here - https://www.evisa.gov.ge/GeoVisa/
Edit:
I tried to apply for eVisa with details you provided. It shows this.
You are exempt from visa!
Holders of valid visa or residence permit of the country you have
selected are exempted from visa requirements. You can enter Georgia
without a visa for 90 days in any 180-day period. Please, note that
you must present relevant valid visa or residence permit along with
your travel document/passport at the moment of crossing Georgian
border. Detailed information on visa free travel is available on the
following website: www.geoconsul.gov.ge.
You can try filling the application and it will tell you.