No act has passed to make the USA a corporation, though a corporation for Columbia was created at this time.
There is a conspiracy theory that has long claimed that in 1871 the District of Columbia became a private business venture owned by bankers, notably the City of London. It implies that the District of Columbia Organic Act of 1871 turned the U.S. federal government into an incorporated private business venture.
More recently, this was adopted by QAnon conspiracy theorists who claim that Trump will be inaugurated on March 4, because America became a corporation in 1871, marking all inaugurations since then invalid.
An article on a site that has espoused a number of conspiracy theories, "freedom-school.com," claims that the Rothschild family struck a deal with the U.S. government to pass The District of Columbia Act to serve its corporate interests.
The theory is tied to disregard the 14th Amendment, which was passed in 1871 and guaranteed rights for all citizens, including former slaves.
Conspiracy theorists have frequently cited 28 U.S. Code § 3002, which includes the phrase "United States means Federal Corporation." This does not take into account the context of the original, legal meaning behind this term, which does not translate to our modern understanding of corporation meaning "business."
There are several different definitions of "corporations" under legal texts, which can occasionally mean any kind of organization or group, and will not necessarily refer to businesses.
A related claim stating that there have only been 18 real U.S. presidents while the rest have been CEOs and that Donald Trump will actually be the 19th president is baseless since there is no such act passed in 1871 to make the U.S. a corporation.
The claim that the U.S. became a corporation on the back of the District of Columbia Act misconstrues its original constitutional meaning and is therefore misleading.