I know that US citizenship is used as the carrot to attract many non-US born (from places like Costa Rica) into service in the US military as OR's but as has been said, I believe you have to already be an American to become an officer.
There was a discussion about this on Arrse a while back and I believe the process involves going through the military attache at the US embassy, having to leave the British military, renounce your British citizenship and serve a minimum of 3 years in the US military.
It could be one of those urban myths things though as everyone seems to know a friend of a friend who had done it.