House cats can carry some infectious bacteria and fungi. Including cat-scratch disease, ringworm, and toxoplasmosis.
First, determine if the wound is deep or shallow.
For shallow scratches: wash your hands with soap, treat with antibiotic ointment and leave uncovered to heal.
For a deep wound or if it’s bleeding badly: apply pressure to stop the bleeding. Then, cover the scratch and see a doctor.
You may require stitches and an oral antibiotic. Cat scratches can be defensive or playful.