Google is working to make its Chrome browser VR-ready on Android. As noted by Road to VR, the latest alpha and beta releases introduce two important components to enable this feature: a WebVR setting which enables enhanced VR device compatibility with VR websites built against WebVR standards, and a 'VR Shell' setting that would allow Cardboard and Daydream users to browse any website regardless of whether it uses WebVR.
The features can be enabled by accessing "chrome://flags" on the URL bar – though the VR Shell is functional just yet, so only websites that are properly equipped to support WebVR will work at the moment – which are not a whole lot of sites right now.
Samsung introduced a VR browser for their Gear VR headset last year which achieves similar functionality, though of course by bringing the features to Chrome it will be available to a much wider audience. WebVR is also being used in Firefox nightly builds.