"to dance in a way that simulates the body's action in copulation," by 2005, alteration of twurk, which seems to have originated in the Atlanta, Georgia, strip club and hip-hop scene and first came to wide attention in the Ying Yang Twins' 2000 song "Whistle While You Twurk," described as "an ode to strippers" ["Country Fried Soul, Adventures in Dirty South Hip-Hop"]. Probably ultimately imitative of something. Related: Twerked; twerking. There is a verb twirk from 1599, "to pull, tug, twirl," what a man does with his mustache, but OED regards this as possibly a misprint of twirl.
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