1840, from ortho- + Greek praxis "a doing, action, performance" (see praxis).
Errata -- Page 263, line 9 from bottom, for 'orthodoxy' read orthopraxy. This is a new coin from the mint of Dr. [Andrew] Wylie [of Bloomington College, Indiana], at least I have not before noticed it. Its etymology places it in a just contrast with orthodoxy: for if that consecrated word indicates thinking right, orthopraxy will legitimately import doing right, and hence, as Mr. Wylie says, orthopraxy in the last dread day will pass the divine ordeal incomparably better than orthodoxy. O! that a zeal for orthopraxy would transcend the zeal for orthodoxy! ["The Millennial Harbinger," vol. iv, no. 8, Bethany, Virginia, August 1840]