Yep. You write them you own them. Post it somewhere that date stamps it,e.g. SoundCloud and don't worry unless it's lawsuit time at which point you can copyright them. Some folks mail the song to themselves and don't open the package.
The only thing that will stand up in court is a copyright from the government. Don't wait until you want to sue as the other party may have copyrighted it themselves and then you are SOL.
According to U.S. copyright law, songwriters own their songs the moment their songs are completed
You would simply have to prove via the posted date that you copyrighted the song. When you put "copyright 2016" beside it it is copyrighted. Really that it. You can then register your copyright at the US office if you choose but that is not required for the song to be considered legally copyrighted. So you aren't SOL. Just in for more of a hassle should it be stolen

Here's a good perspective.
http://www.greatamericansong.com/copyrights.php