https://www.law.cornell.edu/uscode/text/8/1182

Yes.  Yes he has been granted the authority.
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“I would point out historically, that U.S. Code Law 1182, passed in 1952 by a Democratic House and Senate said the President of the United States has authority to bar immigrants from any country, regardless of race or religion if he believes they represent a threat to the United States…

“This was used by President Jimmy Carter to ban Iranians from coming here and was used to deport several thousand Iranian students (after the Hostage taking). … When people call Trump a nut-case for saying ‘no more Muslims until we figure this out’ he stands on law.”
Under the terms of the law, a U.S. President does have the power to ban individuals from entering the country.

You can find this at  http://ethicsstupid.com/personalities/fact-checking-a-reader/