I'm not saying there aren't Trumpkins who wouldn't love to "register" all the Muslims in the US, probably all the Jews and Atheists and Liberals too, while they're at it.. but we should be clear, on terms, as to what is being described- because the media, too, doesn't do a very good job of explaining this stuff.
Trump has talked- inasmuch as he's clear either, which he isn't, I'm sure he has no problem letting his supporters think he really means "registering all the Muslims" - about reinstating a Bush-era program that was ended which tracked Muslims in this country on visas.
It's worth noting that Obama just did something to make that much harder:
http://www.thefiscaltimes.com/2016/12/22/Obama-Just-Made-It-Harder-Trump-Create-Muslim-Registry
The Department of Homeland Security on Thursday officially shut down the National Security Entry-Exit Registration System, a leftover program put in place in 2002 following the 9/11 terror attacks a year earlier. The controversial program required males aged 16 and older who enter the U.S. from specified countries to be fingerprinted, photographed, and interviewed about their plans. The program is also extended to people already living legally in the U.S. if they came from countries on the list.
Of the 25 countries named in the regulation, all but one, North Korea, were majority Muslim nations, leading to charges that the rule was discriminatory. However, the systems own flaws were its downfall. The program turned out to be expensive to implement, unwieldy in operation, and worst of all, redundant.
But, there is one salient point here, which is that the reality would be reinstating of a discredited and found-to-be-useless but apparently legal Bush program of tracking people visiting this country, as opposed to creating some highly unconstitutional registry of US citizens. So saying "add my name to the list" is meaningless unless you're here, say, on a visa.