Moving Files From Dropbox App to Music App

The only ways to get music into Music.app is to sync with a computer, purchase from the App Store or use iTunes Match (which requires a computer to get set up). Unfortunately because of the way iOS is architected it is not possible to take music from third-party apps or websites and put them into Music.app.

Basically, you'll need some computer to import the songs into iTunes. It doesn't have to be your computer, just one that can either sync the tracks to the device or get them into iTunes Match. Once you have the sync, you can delete your songs from that computer.

You can play the songs from Dropbox by streaming them locally using the dropbox app (or mobile safari if you save them to a shared folder) and it will cache the songs locally as long as you have room. But, it's not the same as having them in the music app which is sandboxed and can't see the dropbox files directly.

The only downside to syncing from a second computer is that you'll have to wipe the existing music or manage manual syncing until you have a computer again.

I downloaded Tunebox, it was $4.99. It doesn't allow you add songs to "Music" but it does allow you to play songs from your Dropbox when your device is offline or in airplane mode. It works for what I needed.