In order to recruit the cat you need the item Old Fish which can be gotten from defeating the raccoon in the trash can in front of the principal’s house. This is located up the street from your house and to the right.
You’ll first meet him in Billy’s garage right before your first boss the Clown Animatronic. He’ll walk off to the Cornfield after the conversation, which is just after the boss fight.
He’ll be on an ATV where you can talk to him and give him the Old Fish. After a short conversation, give him the fish and he’ll join you.
Edit: forgot to give the cats location.