Finally much awaited wait is over, today Google releases the official AdSense app for Android and it is available for download in Google Play Store. Right now, this is the first version of official AdSense app for Android, so the app does not have as many features as you want.
According to release notes,
The Google AdSense app provides an easy way to access key data from your AdSense account. Access reporting features anywhere, directly from your mobile phone. The first version of the app gives you access to: the key earnings information, top custom and URL channels, ad units and sites reports, payment alerts.
Right now, this app is only available for devices running Android 4.0 or Android 4.0+.