I have always had that fear too from a stray cat that did bite me as a child.
Several months back, I was in a very similar situation. A cat just started showing up. I started putting food out for him, initially he would run from me, but eventually he got use to me. I would just sit outside with him everyday and just let him approach me. I figured if I let him come to me, he would be less defensive and not bite me. I put a carrier outside for him to get use to, too.
I posted several signs around my area, as well as posting an ad in the newspaper for a found cat. No one ever responded.
I finally got him into the carrier and off to the vet. I contacted several rescue agencies in my area and they posted a pic of him on their web sites. He was adopted within a week and a half of him being posted by a very nice lady, who still sends me updates.
I wish I could have kept him, but two of my boys have issues with their love towards one another. And I just couldnt chance bringing another boy in to perhaps cause more territory issues.
Yours could very well already belong to someone and just really like your food. If you posted some flyers, that would at least give you some ideas as to where to start or if you have anything to start.
There is a neighborhood cat that comes over everyday and I feed him everyday (with his owners permission). I even have a cat bed on my veranda for him to come and nap on. He does have an owner, but I guess he likes my food better.