Stray cat in front of my door

A stray cat came and seemed to be wanting help. I gave it some food
and now it won't leave my front door. If I open the door it tries to
come in the house. It looks like it might be sick, because each of its
eyes has some kind of channel/groove coming down from the inner corner
about half an inch. I just want to know is there any kind of disease I
could catch from this cat if I have to touch it? I've avoided touching
it so far. I just wanted to help it along a bit with some food and to
have it go away. No way do I want to get sick from touching it. I
don't need any trouble. I'm looking for some organization to call to
take it. I'm in southern California.