So this is a debated subject. Different groups claim different things. The co-founder of AIM, Clyde Bellecourt, makes the claim that it was in fact Europeans who invented the practice. It was used in order to show that they had in fact made a kill. It was similar to the practice of cutting off the tail of a gopher to show that you had actually killed it, in order to pick up the bounty. Bellecourt also argues that this is where the term redskin first appeared, in reference to the Indians face being covered in blood. Redskin then was a derogatory term that was in reference to a dead or dying Indian.
While Bellecourt may be partially right (it is very possible that the practice was helped spread by Europeans also doing it), there is evidence that some tribes had already practiced it prior to European contact. For instance, Jacques Cartier reported on the practice in 1535, when he sailed to Quebec City. He was told by Donnoconna, his host, that the scalps he was shown were from their enemies, who they had been waging a war against.
About 3 decades later, the practice was also reported by Jacques Ie Moyne in what is now Florida. So we know for certain that it was practiced along the eastern coast.
Archeological evidence also shows it happening further west. Along the Mississippi and Missouri Rivers, archeological sites have been found that show clear signs of the practice of scalping, particularly the markings left on skulls from the process. In addition to that, we also have other archeological evidence from individuals who survived being scalped, and while healing, formed a telltale scar.
So we can be rather certain it was somewhat widespread. It didn’t exist throughout the continent, at least pre-European contact. After European contact, we know the process became more widespread, being spread by Europeans themselves, and encouraged through bounty prices.