"give motion to by the act of pulling," c. 1200, drauen, spelling alteration of Old English dragan "to drag, to draw, protract" (class VI strong verb; past tense drog, past participle dragen), from Proto-Germanic *draganan "to draw, pull" (source also of Old Norse draga "to draw, drag, pull," Old Saxon dragan "to carry," Old Frisian drega, draga, Middle Dutch draghen "to carry, bring, throw," Old High German tragan "carry, bring, lead," German tragen "to carry, bear"), from PIE root *dhregh- (see drag (v.)).
Sense of "make a line or figure" (by "drawing" a pencil across paper) is from c. 1200. Meaning "remove or extract (a weapon) by pulling" is from late 12c., originally of a sword. Sense of "to pull (a bowstring)" is from c. 1200. To draw a criminal (drag him at the tail of a horse to the place of execution) is from c. 1300.
Meaning "select one (from a number of lots, etc.)" is from c. 1300. Sense of "bring (a crowd, an audience, etc.) by inducement or attraction" is from 1580s. Of a ship or boat, "to displace (a specified amount) of water," 1550s. In card-playing, "to take or receive (a card)," by 1772; draw-poker is by 1850. To draw out "lengthen, protract" is from 1550s; to draw the line in the figurative sense of "make a limit" is by 1793. To draw blood is from c. 1400.
The difference between [Draw Poker] and Poker is, that the player can draw from the pack as many cards as he may wish,--not exceeding five,--which must be given him by the dealer; but previous to drawing he must take from his original hand the game number as he may wish to draw, and lay them in the centre of the table. ["Bohn's New Hand-Book of Games," Philadelphia, 1850]