1580s, "to disturb," from Latin agitatus, past participle of agitare "to put in constant or violent motion, drive onward, impel," frequentative of agere "to set in motion, drive, drive forward," figuratively "incite to action; keep in movement, stir up" (from PIE root *ag- "to drive, draw out or forth, move").
Literal sense of "move to and fro, shake" is from 1590s. Meaning "to discuss, debate" is from 1640s, that of "keep (a political or social question) constantly in public view" is by 1828. Related: Agitated; agitating.