Back in 2015, a liberal law scholar said he could do it.
http://www.nbcnews.com/politics/2016-election/legal-scholar-trump-s-muslim-ban-may-be-constitutional-n484981
Summary:
* we banned communists and marxists from immigrating, due to viewpoints, and it was upheld because First Amendment protections don’t apply to immigrants seeking to come
* if Islam is classified as a group seeking to overthrow the government, it is allowed under national security guidelines
Did FDR seek approval from congress before he seized the lands of the Japanese and incarcerated them in camps?
of course, being a liberal progressive, FDR would have probably been more interested in the seizure of large farmlands than he was in sending them to camps.