early 15c., "a playing card," from Old French carte (14c.), from Medieval Latin carta/charta "a card, paper; a writing, a charter," from Latin charta "leaf of paper, a writing, tablet," from Greek khartes "layer of papyrus," which is probably from Egyptian. Form influenced by Italian cognate carta "paper, leaf of paper." Compare chart (n.). The shift in English from -t to -d is unexplained.
Sense of "playing cards" also is oldest in French. Sense in English extended by 1590s to similar small, flat, stiff pieces of paper. As "small piece of cardboard upon which is written or printed the name, address, etc. of the person presenting it" is from 1795, visiting-cards for social calls, business-cards announcing one's profession. Meaning "printed ornamental greetings for special occasions" is from 1862.
Application to clever or original persons (1836, originally with an adjective, as in smart card) is from the playing-card sense, via expressions such as sure card "an expedient certain to attain an object" (c. 1560).
Card-sharper "professional cheat at cards" is from 1859. House of cards in the figurative sense "any insecure or flimsy scheme" is from 1640s, first attested in Milton, from children's play. To (figuratively) have a card up (one's) sleeve is from 1898. To play the _______ card (for political advantage) is from 1886, originally the Orange card, meaning "appeal to Northern Irish Protestant sentiment."