You do not "copyright" a sign (as in "to copyright", transitive verb). You may register a trademark. But as far as copyright is concerned, once you have given expression to your idea (for ex. committed it to paper if it is writing or a design) then it is automatically protected by copyright.
I would say that the copyright sign cannot be copyrighted or the registered (put after a name to signify a trade mark). I know that inventions have something called a patent. I don't know if simply added a symbol make something copyright or if it has to be registered with somewhere.