What should I do about this cat?

I recently found this cat by my doorstep about two days ago. It's a very small, skinny and possibly young cat that I have never seen before in my neighborhood. I'm pretty sure somebody must have dropped it off because none of the neighbors seem to have claimed it at all. Since it's been cold this p weekend I have been feeding it a little bit, but I am worried that it will soon become a "pet" to my family and I. What should I do about it?