Copyright is a noun meaning an author’s exclusive legal right to his or her work. A copyrighter is a person who secures copyrights. Other forms include copyrighting, copyrights, copyrighted, and copyrightable. Copywrite is not a word. Copywriter—meaning a writer of copy, especially in advertising—is a word. So is the noun copywriting, meaning the work of a copywriter.
Examples
Here are a few examples of some of these words used correctly:
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]