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.