Ownership of a copyright is automatic: it emerges as soon as the work is created. Claiming the copyright and marking the work with the copyright symbol © - even if handwritten - will further establish ownership.
With that said, it is strongly recommended that you register your copyright with the U.S. Patent and Trademark Office. The cost is minimal and registration will help ensure your rights in the event that the work is misappropriated. When a work contains a valid copyright notice, an infringer cannot claim in court that s/he wasn’t aware the work was copyrighted. Thus, an author has a greater chance to win a copyright infringement case and spend much less litigating in the process if s/he has a copyright notice.