Let's face it: the average American colonist was going to worship any scrap of paper that took power away from a king.

The Magna Carta was like their holy grail. It didn't really matter that a lot of the clauses didn't really apply to their situation, they were just totally stoked to not be the first people ever to think that the King of England was a loon who should be stopped from making important decisions and operating heavy machinery.

And yeah, some of the basic ideas from the Magna Carta did make their way into the Constitution, like simply the fact that governments should have some stuff written down beforehand that says what their leaders can and can't do.