I trapped a cat, paid for his neutering and found him a home by posting up pics and asking someone to adopt him on FB. It worked! His name is Shockley and he went from this:
Honestly, I would have let him live outside or found a shelter that is committer to no-kill. Since he is fixed, he is not going to increase the population. He could have been previously trapped by a spay / neuter / release program.
It's not too late to look up no-kill shelters or find an organization that might be able to help you relocate him to an existing feral cat colony. Like I said, since he is fixed, he won't be knocking any other kitties up. Set him free.
Cats belong indoors.