The U.S. military changed over to using Social Security numbers. The Army and Air Force changed over in 1969, the Navy and Marine Corps changed over in 1972, and the Coast Guard changed over in 1974. If you served after the date for your branch, then use your SSN.
If you served in the military before the changeover date for your branch, then your Military Service Number would NOT be your SSN, but you can find it on DD form 214. If you do not have DD form 214, request it from the National Personnel Records Center (National Archives) in St. Louis, Missouri by calling 314-801-0800.