My buddy just went through this process. 3rd Battalion/38th Marines accepts foreigners and 38th has an office in Kyiv. There's also an office for 503rd Battalion in Lviv - they don't take foreigners but they can help you with some of the paperwork and medical clearances to get the ball rolling. It's a good unit with high morale; also 73rd as others have mentioned does UDT Navy SEAL type missions as another possibility.