The QiYi Smart Timer does what I have thought could be done for a few years now, it connects to the QiYi Smart Player app via Bluetooth and then stores all your times in the cloud so you can see your solve time mirrored from the timer to your phone. The app also has a phone timer option which means that you don't need to buy the timer to get unlimited cloud storage of your cube solve times! The timer is available for just £14.

Buy it here if you really want