He ran as a Republican, he won the Republican Nomination for President, he sits in the Oval Office as a Republican. He is a Republican and one whose loyalty is only to himself.
From the Washington Post in November 2015
https://www.washingtonpost.com/news/the-fix/wp/2015/11/07/donald-trumps-got-a-particularly-strange-voting-history/
"And then we introduce Donald Trump. In a weird political world, Trump's voting history probably stands out. Donald Trump first registered to vote at Trump Tower in 1987, a few years after the building was completed. Since then, according to The Smoking Gun, he's been a Republican three times, a Democrat once, a member of the Independence Party once and, for a brief period, had no party identification at all."
"Curious about how often he actually voted, we reached out to New York-based political consulting firm Prime New York which has an updated list of voter behavior in the state. They provided The Post with Trump's history, back to his first registration. During that time, Trump voted in 18 of 28 general elections -- missing seven during the third-year races. He's voted in two of the 11 primaries he could have -- both of those in which he could have voted since 2010. He could have voted in two special elections, too, but didn't."