"I have witnessed people who sit there and dial up their friends to give them a blow-by-blow description of what's happening," said New York councillor Philip Reed, who's behind the campaign.
"Our message is 'close it up, turn it off, put it in your pocket and enjoy the film'," he added.
Most cinema-goers in New York seem to think it's a great idea.
"It's annoying when people in movie theatres start making calls on their mobile phones, you end up missing parts of the film you've paid for," one fan said.
Call the cops
But some cinema staff reckon it'd be impossible to make people stick to the law.
"It's a movie theatre, you can't call the cops and have them come down to fine someone for having a mobile phone," said Nikki Weispeenning, who works at a cinema in New York.