The best thing for this cat is to give her to a no-kill pet rescue organization in your area. It would be best if it primarily was geared towards cats, also. Right now, she is lonely and very much at risk of a human hurting her, or other animals hurting her.
Please, do her a big favor, and help her find a new family. Don't take her to the local animal shelter, unless it is a no-kill shelter. She needs love and she needs to be able to come indoors.