This app was mentioned in 2 comments, with an average of 1.50 upvotes
As a developer, I ported Tuscany Demo from Oculus Rift to mobiles without gyroscope and even without compass, using back camera to detect yaw. It is an expensive demo, if you need a low quality one, contact me.
If you wanna try my app: https://drive.google.com/file/d/0B91dwUR-bwKIc0lZLXR1VnMtZGM/view?usp=sharing
Also, there is an app that uses compass to detect movement: https://play.google.com/store/apps/details?id=com.sriley.game.cardboard
But most of the apps (and the best ones) need gyro to work.
There's this. Uses compass instead of gyro.
I once checked out some internet store and only third of the phones had a gyro and half had a compass. Is this representative of the market? If so, cardboard was supposed to popularize vr, and you can do tracking in many ways that work even on shifty phones, then why does nobody do that?