I thought the USAF would have been a possibility but evidently not:
Contact Us: Frequently Asked Questions - airforce.com
I am a non-U.S. citizen. Can I join?
Enlistment into the U.S. Air Force by citizens of countries other than the United States is limited to those foreign nationals who are legally residing in the United States and possess an Immigrations and Naturalization Service Alien Registration Card (INS Form I-151/551, commonly known as a "Green Card"). Applicants must be between 17 and 27; meet the mental, moral and physical standards for enlistment; and must speak, read and write English fluently.