Robocalls can be legally blocked by a cell phone just as they can be blocked on a land line. The Federal Communications Commission rules require that the receiver of a phone call can opt out of getting future calls immediately through an automated menu.
Additionally, cell phone users can place themselves on the National Do Not Call Registry to prevent any future robocalls. If calls persist, a phone user can file a complaint with the FCC by calling them, mailing them or filling out a form online. Some cell phone providers also allow users to block specific numbers to prevent calls from going through.