While many international students participate in exchange programs to manage the cost of study abroad, most Russian universities don’t offer exchange programs. Traveling to Russia can be quite expensive, but don’t let cost dissuade you! As a Russian major, it will be particularly important for you to apply for scholarships  to fund your study abroad experience, and there is plenty of funding available.
Most of the scholarships available to you will have application deadlines far in advance of your departure, so be sure to apply for funding early. Also note that the Rotary Foundation  is currently a year behind in their application process and should be applied for a year (or two) in advance.