Intransitive meaning "hint obliquely" is from 1560s. Meaning "maneuver (someone or something) into some desired position or condition" is from 1570s. Physical or literal sense of "to introduce tortuously or indirectly" is from 1640s. Related: Insinuated; insinuating.
1520s, "act of making an indirect suggestion;" 1530s, "that which is indirectly suggested," from French insinuation (16c.) or directly from Latin insinuationem (nominative insinuatio) "entrance through a narrow way; an ingratiating oneself," noun of action from past-participle stem of insinuare "creep in, intrude, wind one's way into" (see insinuate).