I usually offer a stray some good quality dried food, as long as their teeth look ok and they dont have bad breath (can indicate tooth decay), if theyre hungry theyll take it. so far i've adopted about a dozen cats over the years from the feral ones at the farm where i live, i can touch them all now, take them to the vet, i've had them all spayed/neutered, the new worm pills that smell like cat treats are ace. i can also take prey off them, i can usually get to a mouse before its injured, its not so easy with birds.
As the lady at the animal sanctuary said, once theyve got over their fright a cat wont turn down food, warmth, safety and medical care. its quite a privilage when a wild one decides it trusts you.