You do not need to register a copyright for your work. Under current U.S. law, copyright protection is automatic and kicks in as soon as a work is created. However, there are some advantages to copyright registration. For example, 

• Registration establishes a public record of the copyright claim by the author
• Registration is necessary for works of U.S. origin before a copyright infringement suit may be filed in court
• Registration within three months after publication or the work or prior to a copyright infringement may make statutory damages and attorney's fees available to the copyright holder in legal actions.

You can find more information on copyright registration at the links from the U.S. Copyright Office below.