While you are on the site, in your browser find and click "Add to Home Screen" A CGN beaver app icon will then be created to your phone that is directly link to the site.
Note: This feature may not be available in some browsers.
More info here. While not exactly common they do show up from time to time in the EE, as Slimbo mentioned. If you're interested maybe post a WTB there--they're not made anymore so you'll have to look for a second-hand one.
