Earlier today, Jagex announced that they will be launching Old School Runescape (OSRS) for mobile devices on October 30th.
The game will be released for both Android and iOS devices. The game offers full cross-platform play with PC, meaning you can play with the same character on both devices.
All players who were part of the members beta, will continue to have access to the game. Since Jagex has already soft launched the android version of the game in Canada, Denmark, Finland, Iceland, Norway, and Sweden, then you can simply download the app in the play store. Unfortunately, everyone else will have to wait for the full launch on October 30th.
Jagex has also opened a Pre-Registration for the game.