"one who is compulsorily enrolled for military or naval service," 1800, perhaps a back-formation (influenced by French adjective conscrit) from conscription, or else a noun use of the adjective.
"to enroll compulsorily for military or naval service," 1813, American English, from conscript (n.). A word from the militia drafts in the War of 1812. Popularized (or unpopularized) during U.S. Civil War, when both sides resorted to it in 1862. Related: Conscripted; conscripting.