Copyright is a noun referring an creator’s exclusive legal right to his or her work. A copyrighter is a person who secures copyrights. Other derivative forms include copyrighting, copyrights, copyrighted, and copyrightable.
Copywrite is a rarely occurring backformation from copywriter—which refers to a writer of copy, especially in advertising. It has never caught on, and some might consider it an error. If you want to say what copywriters do, say not that they copywrite but that they write copy.
Examples
In 1998, in a controversial piece of legislation, Congress extended the length of copyright protection in the United States by 20 years. [New York Times]
I was a copywriter at the time, trying to write an article for a client, a stationery company. [Independent]
Otherwise, why else would they bother to go through the expensive copyrighting process? [Australian]
The description of a film’s protagonist as a “quirky outsider” in the copywriting on the back cover of a Blu-ray does not inspire much confidence. [DVD Talk]