Can A Month Old Kitten Have Rabies. It Is A

can a month old kitten have rabies. It is a feral kitten and when I picked it up its claw scratched me. and it nipped my finger. I am on blood thinners so it did bleed. I immediatelay washed it and put alcohol and neoparin on it . Have been washing it with Hibiclens. It is healing well just very little nicks.