If you only have the file in a phone app, it can be difficult to get it onto the watch.
If it's on the computer, though, you can record it using something like AudioHiJack Pro. Then give it a name, import it into iTunes, put it on a playlist, and sync it to the watch.
I'd recommend assigning a photo as album art to make it look nicer and be easier to find on the watch.
It's a hassle, but if you plan to listen to it a lot, worth the effort.