As the author of a thesis, you already own the copyright to your work. Under U.S. Copyright law, a creator of an "original work" created in a "fixed tangible medium" is immediately and automatically the copyright owner of the work.
Registration with the U.S. Copyright Office is optional but recommended. The registration gives you the right to sue over copyright infringements and allows you to be awarded damages and attorney fees in an infringement action. It also provides some other benefits such as establishing a public record of your thesis and copyright. Registration is required before you can have these benefits.