Historically, no.
Modern times and considerations would compel this.
This is a pretty common theme in dystopian storylines involving superheroes – revelation, registration, recruitment, relocation, regulation, usually prior to some kind of open revolt or revolution against the status quo – particularly since the grim and gritty 1980s, patterned after the particularly unsavory and crimes against humanity perpetuated by the Allies and Axis to members their own internal ethnic groups and politically incorrect populaces during WWII.
Both Alan Moore’s Watchmen and Frank Miller’s Dark Knight Returns allude to it overtly or in passing, as did Chris Claremont in his X-Men run; its been seen plenty of times since, as noted, in the Justice League TV show and The Incredibles. More benign percursors might include the Science Police’s requirement to register alien abilities in the pages of Jim Shooter’s* Legion of The Super-Heroes* stories; Superman’s voluntary revelation to JFK of his secret true identity as Clark Kent; and the Avengers becoming a U.S.-sanctioned group in the stories, all in the 1960s.
Genre conventions of superheroes have pretty much stayed static for seven decades: superheroes follow an extremely rigid code of conduct, and civil authorities give them wide latitude. In most comics, if authorities wanted to question a superhero in a criminal matter, they’d ask him to turn himself in, or ask another superhero to bring in the hero of interest. Convential city and state authorities simply cannot reign in a rogue superbeing.
No modern government would extend that kind of autonomy soley on the basis of someone’s promises to behave themselves. For one thing, we don’t have that kind of trust or precedent.
Yet no modern government can compel anyone to mandatorily register without the appropriate resources in place to monitor and enforce that law, either. How could you MAKE a superman register? How could you PUNISH a wonder woman for defying the law? Would non-compliance be a misdemeanor, felony or capital crime? A state or federal matter? Would it depend on your demonstrated power-level classification?
It would be regulatory mess. Civil libertarians would love it. If this were a policy that was to be implemented now, if superheroes had been in existence for 70s years, I doubt it could be implemented unless there was a major scandal that polarized public opinion, as the traditions and past policies of this nation towards superheroes give them incredible autonomy. But all things change, and i’ts possible some regulation could be warranted.
If this were a policy that was to be implemented now, as if superpowered beings were a recent discovery, you could very likely get superheroes designated as a special class that require registration and regulation. When you deal with superheroes of a certain power range, this is a justifiable policy. If superpowered beings are excessively more powerful than your ability to monitor or enforce to obey the law, then the law becomes flawed.
One safe bet: all extraterrestrial beings, artifacts and transport systems would fall under federal statutes and military jurisdictions and NO private citizen could claim rights to. A natural-born citizen with powers would have inalienable rights that some guy who picked up a magic hammer wouldn’t.