Both the U.S. Copyrighting Office and the WGA provide copyrighting services for a fee. However, in the United States, the creation of an original work confers an automatic copyright. No further registration is necessary.
I don’t know any writer (and I know a lot of writers) who has ever witnessed theft. If your idea is worth stealing, Hollywood is going to want to work with you! That said, it’s easy to provide your own proof of creation; just mail a copy of the script to yourself. As long as the envelope remains sealed, the postmark proves your date, should litigation arise.