Personal music can be used as a ringtone on the iPhone, but it must be converted to a specific format first. To do this, a Windows computer with iTunes installed, or a Mac, is needed. Unfortunately, as of September 2014, there is no way to customize ringtones without a computer.
First, the song file must be assessed to confirm it is a valid format. MP3s and M4As are valid formats. Determine the section of a song you want to use as a ringtone, and select it by right-clicking the file in iTunes, clicking Get Info, and going to the Options tab. Then, right-click the file again and click Convert Selection to AAC. Go to your library and find the newly created file. Right-click and select "Show in Explorer/Finder" and change the extension of the file to .m4r. Drag the new .m4r file to iTunes and sync it with your iPhone.