c. 1600, "act of carrying off" as prey or plunder, from rapt + -ure, or else from French rapture, from Medieval Latin raptura "seizure, rape, kidnapping," from Latin raptus "a carrying off, abduction, snatching away; rape" (see rapt). The earliest attested use in English is with women as objects and in 17c. it sometimes meant rape (v.), which word is a cognate of this one.
The sense of "spiritual ecstasy, state of mental transport or exaltation" is recorded by c. 1600 (raptures). The connecting notion is a sudden or violent taking and carrying away. The meaning "expression of exalted or passionate feeling" in words or music is from 1610s.
"to enrapture, put in a state of rapture," 1630s (implied in raptured), from rapture (n.). Related: Rapturing.