Do you have to copyright your book?
You can (and should) include the © symbol in your book’s front matter. But once you write your book, you automatically own the copyright.
According to the US Copyright Office:
“Your work is under copyright protection the moment it is created and fixed in a tangible form that it is perceptible either directly or with the aid of a machine or device . . .
“In general, registration is voluntary. Copyright exists from the moment the work is created. You will have to register, however, if you wish to bring a lawsuit for infringement of a U.S. work.”
You can absolutely pay to copyright your book with the Library of Congress. The standard application fee is $65.
And if you ever want to sue someone for piracy or infringement, your copyright should be registered. Learn more about copyright straight from the source.
Just know that even if you choose to skip the copyright fee, your book still belongs to you.