Oh Trump has blubbered about it enough that I would take it seriously.
It wouldn’t be a legal mechanism if there was something stopping him from doing it.

(from the article)

“We’re losing a lot of people because of the internet,” Trump said. “We have to go see Bill Gates and a lot of different people that really understand what’s happening. We have to talk to them about, maybe in certain areas, closing that Internet up in some way. Somebody will say, ‘Oh freedom of speech, freedom of speech.’ These are foolish people. We have a lot of foolish people.”

“ISIS is recruiting through the Internet. ISIS is using the internet better than we are using the nternet and it was our idea,” Trump said. “I want to get the brilliant people from Silicon Valley and other places and figure out a way that ISIS can’t do what they’re doing. I would certainly be open to closing areas where we are at war with somebody. I sure as hell don’t want to let people that want to kill us and kill our nation use our Internet.”

When challenged, he added: “I’m not talking about closing the internet. I’m talking about closing parts of the internet where ISIS is.”