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.
Jerrie Cobb
Although she never flew in space, Cobb, along with twenty-four other women, underwent physical tests similar to those taken by the Mercury astronauts with the belief that she might become an astronaut trainee. All the women who participated in the program, known as First Lady Astronaut Trainees, were skilled pilots. Dr. Randy Lovelace, a NASA scientist who had conducted the official Mercury program physicals, administered the tests at his private clinic without official NASA sanction. Cobb passed all the training exercises, ranking in the top 2% of all astronaut candidates of both genders.
In 1962, Cobb was called to testify before a Congressional hearing, the Special Subcommittee on the Selection of Astronauts, about women astronauts. Astronaut John Glenn stated at the hearing "men go off and fight the wars and fly the airplanes," and "the fact that women are not in this field is a fact of our social order." Only a few months later, the Soviet Union would send the first woman into space, Valentina Tereshkova. Soon afterward, Tereshkova ridiculed Cobb for her religious beliefs.