Drafting was the act of forcing someone to enlist in a military, often without their consent.
In the 2270s, an upset Doctor Leonard McCoy protested his reinstatement under the reserve activation clause, clarifying "in simpler language, Captain, they drafted me!" (Star Trek: The Motion Picture)
In 2373, Neelix asked Kathryn Janeway's permission to accompany a rescue team that was trying to locate Kes, giving his combat training and willingness to make the mission a success as reasons why he ought to go. She agreed, saying "Consider yourself drafted." (VOY: "Warlord")