New Cat - No Name Yet

This 6 month old cat showed up in my backyard last week. She was stalking my birds and managed to kill several of them.
After 5 days, she was still there, no matter when I looked out the window. We realized she was trying to survive.
We fed her outside for a few days while contacting local papers, Craigs List, and various Animal Shelters.
No one has claimed her. I finally brought her in the house. She has no desire to go back out, which is fine with me.
We have a lot of coyotes running at night. It is very dangerous for cats to be outside, as coyotes just love a cat snack.