As long as a marriage is not fraudulent - and immigration will scrutinize information to weed out fraudulent claims - and there are no other reasons for exclusion, an American citizen may bring a foreign spouse into the US because he or she is considered a qualifying "immediate relative."
Also, lawful permanent residents - green card holders - may bring a spouse into the US on a permanent basis. But this is subject to a quota system which can take years.
If you are a homosexual and your partner is a foreign national living abroad, then your opportunities to permanently bring your partner into the US plummet. True, the trend is that some states legally recognize the rights of same-sex couples. But immigration law, which is federal law, does not protect you.
Recently, the State Department carved a very narrow exception for same-sex partners. The catch? The exception protects diplomats only.
If you are a diplomat that is posted in the US, then your foreign same-sex partner may get a visa to get into the United States.
What would typical same-sex couples do to stay united? Your best bet is to immigrate into the US on other grounds, especially if you can find a US employer and you intend to work and live in the US permanently. See an immigration lawyer to look at alternative solutions.