In Trump's Travel Ban Executive Order, the laws he is executing with the order are listed. Among them is a law that gives the President the ability to prohibit persons from entering the United States if he believes they may be a danger to the national security of this country.
Article I, Section 9 of the United States Constitution authorizes Congress to make laws prohibiting persons from "migrating" into the United States with legislation.
Based on the original intent of the United States Constitution, Trump's travel ban regarding a few Muslim-majority countries who have proven they are sponsors of terrorism, and are willing to harbor terrorists, is completely constitutional.