When you adopt a cat that has lived on the street for some time, and has adapted to such a lifestyle, you first need to understand that the cat will most likely need some time to warm up to you. Feral cats develop a natural wariness of humans and may feel some fear in a new home. It is important for the new owner to provide the cat with what he or she needs to feel safe, as this will provide the foundation that is necessary to establish trust.
When you first acquire your formerly feral cat, he or she will need an enclosed room away from other members of the household. It is important that this room have all of the cat's needed supplies and that it include a place to hide from people if he or she feels afraid. The new owner can then begin to gradually introduce himself or herself to the cat.
A feral cat may need the new owner's first few interactions to be indirect. The owner can start to become a familiar presence by bringing food and staying in the space for a while, then later by sitting casually in the room while the cat gets used to him or her. When the cat seems to be more comfortable with the owner's presence, the owner can offer a toy or extend a hand for the cat to smell.
When the cat begins to rub on the owner, this indicates that the cat is ready for contact. With more time and gentle interactions, the cat may be ready to leave the safe space or meet other family members.