SIMFEROPOL, Ukraine—A week ago, Dmitry Polonsky was a fringe political activist in the Ukrainian province of Crimea, signing up middle-aged men rankled by the new authorities in Kiev to a small pro-Russia militia.

Today, as thousands of Russian troops swarm through Crimea, Mr. Polonsky's star is rising. He introduces himself as an adviser to Crimea's new prime minister. His Russian Unity party, though holding only three of 100 seats in the regional assembly, is the de facto authority in the Black Sea peninsula that has cut...