Will my cat get arthritis when she hits old age?

Awwww she is a cutie. I applaud you for taking her in when no one else wanted her. It brought a tear to my eye. As far as your question goes though, there is really no way to tell if she will get arthritis or not. She may be more prone to it because of her accident or heredity, but there is really no way to tell. Keep taking good care of her, she looks like a really happy kitty :)