Can a Russian woman just travel to U.S.A and marry a man?
I have been in contact with a Russian woman who would like to come visit me. Can she do that? And while she is here and if all is well could we just get married?
Disclaimer: I am not an immigration attorney and you should not make any decisions that rely on this advice being true. But I have dealt with USCIS before and have some experience with their policies. I recommend verifying everything I say at the USCIS Website.
I have two answers to your question, one to the exact, specific question you are asking, and one for the question you probably should be asking.
First, the literal answer. Can a Russian woman "just" travel to the U.S.? Not "just"... Not like U.S. citizens can "just" travel state to state, or to the U.K. or France. A Russian woman needs a visa to enter the U.S. And unless she is one of the rare recipients of a work visa or student visa, the remaining options are tourist visa, fiancee visa, and spousal visa. The Fiancee visa requires that you have already met her in person and are already engaged to be married and can provide a TON of evidence proving this meeting and engagement. The spousal visa requires that you are already married (like if you traveled there to marry her and want to bring her back) and can provide a TON of evidence proving your marriage is real.
But, the closest thing to her "just" coming over is the tourist visa. I know tourist visas for Russian/Ukrainian women are a little less rare than they used to be, but they are still fairly rare.
I strongly suspect that if you met a Russian woman who legally came to America (using one of these visas), you could marry her, and there is a method to allow her to stay here and apply for residency and then citizenship. I'm quite certain that this would be a much more complex immigration process than if you met a girl in Russia, got engaged there, then applied for a fiancee visa (and that process is already very complex).
Now the "other answer". I hate to rain on your parade, but if your case is such that you met a Russian woman online and have been emailing back and forth for a few weeks or months, and she sounds very in love, and is very eager to finally come be with you, and is saying that she has (or can obtain) a visa to visit America, BUT she needs you to wire her money for flights and/or visa fees, there's a 99.9999% chance that it's a complete fraud (and that's an optimistic estimate ;-) and you would never see her or your money again. Well, you might see her emails again if she feels she can get even more out of you!
Have you seen her on a video call (like Skype)? Have you met in person? Have you seen her friends?
My whole site is all about the subject of meeting and marrying a Russian woman and avoiding the ubiquitous scams that plague the path.
Since you are already in communication with this one, I recommend you start by reading my page on Russian Dating Scams and every link referenced in it, especially the sections and pages about Email Scams.
THEN I would strongly recommend you read the questions other readers have posted and my answers about scams at Russian Scams Q & A.
If you can get through that "assigned reading" and have no doubts that your girl is the real deal and there's no chance that it's a fraud, then you may be one of the lucky ones!
I hope that answers your question.