Could I join you?
Can I join you?
Can I accompany you (to a particular place or activity)? You guys are going bowling tonight? Can I join you?
Could I join you?and (Do you) care if I join you?; (Do you) mind if I join you?
Will you permit me to sit with you? (An inquiry seeking permission to sit at someone's table or join someone else in some activity. Also used with can or may in place of could.) Tom came into the cafe and saw Fred and Sally sitting in a booth by the window. Coming up to them, Tom said, "Could I join you?"