"carpenter who makes carts," early 15c. (late 13c. as a surname), from cart (n.) + wright (n.).
Entries linking to cartwright
cart n.
c. 1200, "two-wheeled vehicle," usually for one horse and often without springs, from Old Norse kartr or a similar Scandinavian source, akin to and replacing Old English cræt "cart, wagon, chariot," perhaps originally "body of a cart made of wickerwork, hamper" and related to Middle Dutch cratte "woven mat, hamper," Dutch krat "basket," Old English cradol (see cradle (n.)).
Many old allusions are from the cart being used to convey offenders to the gallows (and sometimes serving as a drop for hangings) or for public exposure, especially of lewd women, either in the cart or tied to its tail. Compare tumbrel. To put the cart before the horse in a figurative sense "reverse the natural or proper order of things" is from 1510s in those words; the image in other words dates to mid-14c.: put the plow (sull) before the oxen.
wright n.
Old English wryhta, wrihta (Northumbrian wyrchta, Kentish werhta) "worker," variant of earlier wyhrta "maker," from wyrcan "to work" (see work (v.)). Now usually in combinations (wheelwright, playwright, etc.) or as a surname. A common West Germanic word; cognate with Old Saxon wurhito, Old Frisian wrichta, Old High German wurhto.
The metathesis of an -r- and a vowel in words from Old English also can be seen in thrash, thresh, third, thirty, bird, wrought, and nostril.
Smith was the general term for a worker in metals, and wright for one who worked in wood, and other materials. Hence, in the later English period, smith (which, in Anglo-Saxon, when used without any characteristic addition, was understood as applying more particularly to the worker in iron,) became the particular name of a blacksmith, and wright of a carpenter, as it is still in Scotland. [Thomas Wright, "Anglo-Saxon and Old English Vocabularies," 1884]