Sure you can, what an issue to think about. Quite simple, you definitely can befriend even a wild cat. The most important thing is that you need to befriend them. This is essential.
You need to see the difference between a stray cat and a feral cat. They are quite different. The stray cat is a cat whom someone used to keep previously, like a former cat that has not got a home anymore; while a feral cat is totally wild, born in the wild nature. This type of cats varies from humans and cannot be adoptable as generally it is not adapted to people, its habitat is wild nature and not a cozy closed home, closed space. While stray cats can be befriended with some effort, feral cats will not get used to your presence.
I, as an experienced cat owner can tell you that keeping a cat is not that easy. It requires much effort and time but it is definitely worthwhile. If you want to make the adaptation process, period easier and smoother, you need to do your best in order for your cat to feel as a part of the family and behave accordingly. From the first sight cats may seem a little aloof, highly independent or maybe indifferent. You just need to understand their psychology. After that you will realize how friendly and cute they are. I am saying this from my own experience of keeping 7 cats. After the period when she totally trusts you she will show her live and respect towards you, how much she loves you. One thing is clear and proven. Cats feel how you feel about them, if you truly love your cute and fluffy kid then you will get the same. If you have some time to spend with your cat, you will get the feedback at once. How to make sure your cat feels comfortable at your house? These signs will illustrate that your cat simply loves you and feels comfortable with you in her new family.