I found this on-line: https://vetexplainspets.com/can-i-get-rabies-from-a-cat-scratch/
The article says: "According to the Centers for Disease Control and Prevention (CDC), it is possible to contract rabies from a cat scratch, but it is extremely rare. Rabies is most commonly spread through the bite of an infected animal, as the virus is present in the saliva. However, in rare cases, the virus can also be present in the saliva of an infected animal and transmitted through a scratch or open wound."

Several years ago I lived in an area where there were a lot of bats flying around at night. I was outside at dusk and bent down to pick up something. When I stood up, a bat flew into my hair at the nape of my neck. It took about 30 seconds for me to use my hand to get it out of my hair. I saw my Dr immediately who suggested I get rabies shots since the bat may have scratched me and they are known carriers of rabies. I had to get several shots over a period of a few days, into a muscle. The shots were not painful. I would see your Dr. Personally, I would treat this seriously since rabies is fatal.

Also, I was at my vet's after this event and a lady came in and said she was bitten by a stray cat and was worried about rabies. The vet told her the only to determine whether the cat had rabies before showing symptoms would be an autopsy of brain tissue.