1622, "Spanish method of capital punishment by strangulation," from Sp. garrote "stick for twisting cord," of unknown origin, perhaps from O.Fr. guaroc "club, stick, rod, shaft of a crossbow," probably ultimately Celtic. But possibly from Frank. *wrokkan "to twist" (cf. M.Du. wroken "to twist"). The verb meaning "to execute with a garrote" is from 1851; sense of "choking and then robbing" is from 1852.
"I have no hesitation in pronouncing death by the garrot, at once the most manly, and the least offensive to the eye." [Major John Richardson, "British Legion," 1837]