Short answer is yes. There is no US law that prevents a US citizens from joining a foreign military. However, if a US citizen were to join a foreign military that was doing something against US interests, the US citizen in that foreign military would face possible charges of treason on US soil.
There are no international militaries, there are only national militaries. If by "international" you mean foreign, there is nothing in American law that prohibits an American to leave his country to become a citizen of another country or fight for another country. Many American Jews can be found in the Israeli military. Americans can also be found in the French Foreign Legion.
The criteria to join the Canadian Forces is either citizenship or permanent residency/ landed immigrant status.
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