From the Editors of The Daily Cat
People will often feed feral cats without thinking of the consequences. Frequently, such cats do not receive proper medical care -- including spaying and neutering -- leading to all sorts of unintended problems.
If you are concerned about picking up the cat, use a humane trap -- shelters often carry Havahart traps that you can borrow -- and get the cat that way. (When dealing with a large family of feral cats, I bought a few of these traps and rented a couple of them from local shelters and pet stores.) Next, take the cat to a veterinarian for a thorough medical examination. Depending on the cat’s age and condition, it might need to be spayed and treated for fleas, ear mites and other issues that cats tend to develop when outdoors.
Your cat sounds gentle enough, but some feral cats need to be confined to a safe and more manageable part of the house while they are being socialized. The organization Stray Pet Advocacy advises that you set up a dark room that is fully cat-proofed, with hiding places, food, water, toys, two litter boxes filled with organic-only potting soil, and articles of clothing that bear your scent placed in appropriate places around the room.
The cat should be allowed to stay and relax in that room for 24 hours as it gets used to feeling safe and secure indoors and around people. You can then gradually begin to play with the cat, pet it and hold it. When it seems comfortable with you and its new life, you can then allow it into the rest of your home.