Zangief is most likely not gay. The rumour came up solely through a mistake in a fan made guide to the Street Fighter storyline. It is called the Street Fighter Plot Canon Guide (usually called “the plot guide”) and is put out by users of the Shoryuken.com Forums, a fan forum on Street Fighter. It was started by TiamatRoar who collected lots of bits and pieces and got a lot of information by Saiki. Now it is being updated by vasili10 who did many of the translations from Japanese to English. Then the rumour spread all across the internet and gay gamers loved to hear that Zangief was officially gay. Some even claimed the two designers officially confirmed it, which is not true, I doubt they were ever asked.
Saiki claimed that Zangief was gay and several sources were given: The Fan Book (ISBN 4-09-121878-4), the SFII Dash special by Gamest, Zangief's SFZ2 ending and his SFZ3 quick bio.
I own the two books and I showed it to people who study Japanese and to actual Japanese and none of them could find anything gay. Zangief and The Great Man (who resembles Gorbachev) are very good friends. According to the Fan Book they even wrestle toghether. I’m not sure wether this book is really canon conform but either way, nothing gay.
Since the first three pieces of evicence are all based on the misinterpreted relationship of the two Russians, there remains Zangief’s SFZ3 bio that claims, he doesn’t like young beautiful women. It is worth nothing that SFZ3 was released more 7 years after Zangief’s first apperance, at least until then, nothing gay bout him was mentioned. In this very game, Zangief meets Rainbow Mika, a young beautiful woman and teams up with her, fighting Shadaloo. I guess this has something to do with why it was added to the bio, but it’s not clear. A Japanese website dedicated to Zangief states the claim as a hoax.
His ending in Capcom Fighting Jam/Capcom Fighting Evolution featuring him bathing with young beautiful women, drawn by Udon, can hardly be seen as a proof for his heterosexuality, as it wasn’t done by Capcom. But they must have at least approved it and since they're keeping track of everything including Posion’s changing gender in the US and Japanese versions of the game, one would expect them to not approve this ending, if he was gay. But who know’s. For this discussion I’d ignore it.
At the time I first read the rumour in the plot guide, it was stated as a fact, without giving any sources. I pointed it out and it was changed. Back then, when I googled for the two terms “Zangief” and “gay” nothing but the plot guide and quotes from the plot guide appeared, and that includes every single google result.