Opsu is an open-source version of osu! written in java and it is now on the play store. You can download beatmaps from anywhere you want and play them on your phone, and even post your scores on leaderboards to compete with friends!

Opsu is published under the GNU GPL v3 licsence
The code for Opsu can be found here:
https://github.com/itdelatrisu/opsu
Opsu's fork for android is here:
https://github.com/fluddokt/opsu
Code for this app:
https://github.com/AnirudhRahul/opsu-Android
Credits for everyone who contributed their artwork to this app are here:
https://github.com/itdelatrisu/opsu/blob/master/CREDITS.md