I should have noted that on the BMI link I just posted, there is another link to their pages called "The Songwriter's Toolbox", where you can read about copyright law in the US, and use a copyright form to copyright your song in the US. The form is in PDF, so you need Acrobat.

To go directly to the government page:
Here is the page of the US copyright office procedures. There are several different ways to copyright music. Scroll down under performing arts, to music, lyrics, recordings. etc.
Copyright Registration Procedures

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