Is monogamy legal in the US?

Yes. There is nothing stopping you from having many partners. However, you may only legally marry one person at a time. If you marry more than one, you are guilty of bigamy, trigamy, and so on.

However, be cautious of your state's bigamy laws... Some bigamy laws also apply to 'common law' marriages, meaning that if the public percieves you to be married to multiple partners or if you live with multiple partners, even if you are technically not married, then you can still be convicted. The good news (at least for those who want to practice polygamy) is that most states don't have the money or time to search out and convict people for bigamy, they have plenty of murderers, rapists, child abusers, and so forth to go after.