Steam recently released a mobile app.
What is confusing is it doesn't say anything about beta, but when you try out the app it says "Account not part of the beta."
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The Android app page says the beta is now open to all registered Steam accounts.
It is in closed beta right now.
From the Steam forums:
Those who wish to join the beta just need to download the Steam app (free of charge) and log in to their Steam account via the mobile app to express interest in the beta. Gamers will be added to the Closed Beta as the service ramps up.
So basically, download the app, open it, and sign in. Signing in lets Valve know you are interested in the beta, and if you are lucky, eventually you will be given an invite to the beta.