Ya. My cat had a bird recently. It was in shock so I did not bring it inside, I put it in the garage in a cardboard box, and put leaves twigs and sticks around the box, plus a heating pad hidden on the bottom. I managed to save the bird but it was a difficult thing to do- it’s only injuries where some broken pin feathers, but I was afraid it would die of shock or maybe a hidden injurylIt worked! looks like a wild rabbit to me. Probably best to try to clean its wounds now while it's in shock, like @Awakening Forest suggested, so it doesn't try to resist you. It seems to be an adult as well.