In my opinion, there's two different waves of Russian Immigration to the United States.
The first significant wave of Russian immigration to the United States was probably during the 1880's, when thousands of Jewish Russians fled because of nasty pogroms occurring at home. Most of them settled in East Coast cities, mainly Boston and New York. Many of them were tied to the Labor Movement, so I'd guess that the first wave of Russians were probably heavily Democratic if it came down to the two party choice. Russians were pretty prevalent in socialist and anarchist circles though.
I'd also wager they supported Teddy in 1904. They also probably swung to the Bull Moose, or maybe Debs in 1912.
The second wave, which arrived during the 1920's, is a very different story. The first wave were mostly oppressed minority victims of Imperial Russia. The second batch were mostly Middle to Upper Class refugees trying to escape the Soviet Union. One of them was even Kerensky. I'm going to guess that these groups would probably go Republican until the Great Depression.
There were also a lot of Russians who arrived in the 1990s after the collapse of the Soviet Union.
