Miranda isn't a law in the US; it's a court decision. So what we call "Miranda rights" are the rights ensured by a legal decision called Miranda v. Arizona, from 1966. It's an abbreviation.
Interestingly, Congress hated Miranda. They passed a law in relative short order saying, no, Miranda's remedy is not legally mandated. But most jurisdictions like Miranda; they make confessions stickier. So it wasn't until the 90s that the little-publicized federal statute was used against a Miranda claim in either the fourth or fifth circuit. This is where it gets kind of interesting.
Rehnquist had claimed, every single time it came up, loudly, assholishly and in complete contravention to the statements of the sitting justices who wrote the decision, that Miranda was *not* constitutionally mandated-- it was a judicially created remedy to a fifth amendment violation. The difference is that Congress may overrule a judicial remedy. It may not make a law overruling a constitutional requirement.
But when the federal statute overruling Miranda came up for review after the fifth or fourth circuit upheld it, Rehnquist made a complete 180 without any justification whatsoever. No way was he going to allow Congress to overrule the Court on his watch-- even if it meant a completely hypocritical decision. So Miranda was then declared a constitutional requirement.
This is why I hate Rehnquist. At least Scalia is intellectually consistent.