Astronaut
The first civilian in space was Valentina Tereshkova aboard Vostok 6 (she also became the first woman in space on that mission).
Tereshkova was only honorarily inducted into the USSR's Air Force, which did not accept female pilots at that time. A month later, Joseph Albert Walker became the first American civilian in space when his X-15 Flight 90 crossed the line, qualifying him by the international definition of spaceflight. Walker had joined the US Army Air Force but was not a member during his flight. 
The first people in space who had never been a member of any country's armed forces were both Konstantin Feoktistov and Boris Yegorov aboard Voskhod 1.
Women in space
In addition to U.S. citizens, US rockets have launched international astronauts. Roberta Bondar (in 1992) and Julie Payette (in 1999 and 2009) from Canada, Kalpana Chawla of India (1997 and 2003), and Chiaki Mukai (in 1994 and 1998) and Naoko Yamazaki (in 2010) of Japan flew as part of the US space program.