Contact your County Extension office and let them know you have great concerns about a possibly rabid or diseased feral cat near your house. There should be some agency that is in charge of taking care of animals like that.
You can try to trap it in a large live trap (like a Hav-a-hart). Use smelly canned cat food or canned sardines for bait. Put a big pile of catnip in the trap too, put it on the trip pan. You can also put a live chicken in a wire cage, cover the cage with brush, cardboard, or feed sacks, and set the live trap right next to it, so the only way the cat has to reach the bird is by going through the trap. Of course, make sure the wires of the cage & the trap are tight enough to keep the cat's paws from reaching through.
I lost a lot of adult birds, ducks & chickens, to a bobcat and a big feral cat this summer. They took the birds without leaving a trace.