1849, from drop (n.) + kick (n.). As a verb by 1874. Related: Drop-kicked; drop-kicking.
Who would linger by the fire, nor from toil an hour snatch
When villages play football in a merry monster match;
E'en a mere ale-drinking Saxon feels some fervour in his soul
As he watches and bets glasses on a drop-kick at the goal.
[from "A Lay of English Field Sports," by "Colonel Chasse," in "The Sporting Review," June 1849]