You can, but it's not necessary to. Just mail yourself a copy and keep it unopened so the postmark will let you know when it was created, and then send it to a publisher.
I'm not entirely sure of copyright law, but techinically, your manuscript is copyrighted the moment you created it. Getting a copyright for it will help you try to recover some money for it, but it is unlikely you will recover any monetary damages for an unpublished manuscript.