CuteSpotify makes it possible to listen to your Spotify songs on Ubuntu Touch. It’s based on MeeSpot (a MeeGo Spotify client), which I’ve updated to make use of Qt5 and Ubuntu’s QML components. It’s still a little rough around the edges but most of the core functionality is in place now.
One particular problem to look out for is that because of the way Ubuntu Touch currently handles applications CuteSpotify has to be kept in the foreground and the phone has to be kept switched on for music to play (otherwise the application gets suspended). Approaches for handling applications that need to keep running are currently being debated, so hopefully that won’t be the case in future version of Ubuntu Touch.
As a temporary workaround, if your phone is in developer mode (achieved by connecting it up to the Ubuntu SDK) you can run “sudo service powerd stop” (default password is phablet) to stop the phone from going to sleep while you’re listening to music, then “sudo service powerd start” to resume normal power management when you’re done. (See popey’s comment for an alternative method).
To install CuteSpotify on Ubuntu Touch simply search for “CuteSpotify” on your phone and it should appear.
The source code for CuteSpotify can be found here: https://github.com/Elleo/cutespotify