Since using iTunes/Music for this is apparently more than some are willing to put up with I did a bit more research and on a Mac it is even easier than what I suggested at first.

Step 1: create an aac-encoded file with the .m4r extension to its name

Step 2: connect phone to Mac and drag and drop .m4r file on to iPhone on desktop

Step 3: there is no step 3

For those who want to do this without needing a Mac or PC there are apps that will do the job as well.

But Finder now has the syncing component for the iPhone, the Music app is only for playback and library management.