1825, "strike with a sweeping motion," from swipe (n.). The slang sense of "steal, pilfer" appeared 1885, American English; earliest use in prison jargon:
The blokes in the next cell, little Charley Ames and the Sheeney Kid, they was hot to try it, and swiped enough shoe-lining out of shop No. 5, where they worked, to make us all breeches to the stripes. [Lippincott's Magazine, vol. xxxv, June 1885]
Meaning "run a credit card" is 1990s. Related: Swiped; swiper; swiping.