You cannot natively download an official Android version of The Binding of Isaac: Rebirth because one does not exist. Until Nicalis announces a port, your only safe options are streaming from a PC or playing the vastly inferior Flash version via a web browser.
Edmund McMillen has confirmed in the past that while an iOS version exists (sold as a premium app), an official Android port has faced technical delays and optimization issues. Any website claiming to offer a direct ".apk" download for a "full version" is likely distributing a fake, a virus, or an unlicensed, buggy port. Download The Binding Of Isaac Rebirth Android
But what about Android?