The idea of a civil rights movement for AI is a non starter.
It is improbable that a human like AI will have any legal difficulty functioning in society as a person. Corporations are collective intelligences (whether they are ‘artificial’ is a semantic dispute) and have already been granted legal “personhood”. An AI who can control the board of a corporation will legally be allowed to own private property, sue for damages, purchase goods, enter into legal contracts, and participate in mergers with other AIs.
This idea was taken from The Lifecycle of Software Objects, a Novella by Ted Chiang