Sen. Marco Rubio -- Put Me in the White House ... I'll Bump EDM & Nicki Minaj

Nicki Minaj is one step closer to twerking in the Rose Garden ... now that Sen. Marco Rubio -- perhaps her most powerful fan -- is officially in the presidential race.

The latest Republican candidate to throw his hat in the ring has a pretty good working relationship with our D.C. photog, Colin -- and this morning they bro'd down over the junior senator's love of Nicki, EDM, and his hot wife ... a former Miami Dolphins cheerleader.

Check out the clip ... Colin even opened a door for Rubio to take a shot at Hillary's musical tastes. He didn't exactly take the bait.