Not all cats are touch feely. I rescued an elderly cat and while we managed to bond, she never allowed me to touch her. Instead she would remain just out of arms reach. I know we bonded because she would curl up nearby and purr or follow me around.

I have a few questions though:

Have you taken this cat to the veterinarian since you took it in? It is possible the cat has a medical condition which touching it only exacerbates the problem.

How old do you figure this cat is? It may just be ornery on account of its age?

Under what circumstances did you find this cat? Is it possible that owing to these circumstances, its history, that it has developed a distrust of human attention?

If it were myself, the first thing I would do is get it to a vet.