Mithya Ji, there was a Pilot program called MAVNI until last year that allowed foreign born nationals to join US Army if they possessed selected languages skills. As you know, you need to be a US Citizen to serve in the military, so if you join through Green Card or through MAVNI program in the past, they will give you citizenship at the end of your training (length of training varies with your job you choose in the army).
Long story short, MAVNI program is closed right now and there is no sign of reopening. So, I suggest you to forget about it and find your alternatives to stay here.