late 14c., narcotik, "substance which directly induces sleep or allays sensibility and blunts the senses," from Old French narcotique (early 14c.), noun use of adjective, and directly from Medieval Latin narcoticum, from Greek narkōtikon, neuter of narkōtikos "making stiff or numb," from narkōtos, verbal adjective of narkoun "to benumb, make unconscious," from narkē "numbness, deadness, stupor, cramp" (also "the electric ray").
This has been connected to a PIE root *(s)nerq- "to turn, twist," with cognates in Germanic (Old Norse snara "to turn, swing, wind;" see snare (n.1)), but Beekes finds this "semantically far from convincing," and writes, "The structure of this word looks non-lE. Therefore, we should rather assume a Pre-Greek word *nark-." Sense of "any illegal drug" first recorded 1926, American English. Related: Narcotics.