It's never been used, but the president has the power to order a shut down of cell service.
On the other hand, while it is a federal crime, organized protest groups could disrupt cell service with jamming devices. Such devices are easily purchased and deployed.
In order for the president to shut down cell service, he or she would have to invoke the Civil Insurrection Act, which gives the power to order cell service providers to shut down.
The Federal Communications Act could also provide an exception for police during emergencies. Technically, police could go to cell providers and say the emergency requires services to be suspended. That has never happened.