I upgraded my Surface RT to Windows RT 8.1 RTM tonight. It's not as easy as a regular Windows 8.1 upgrade, and it has some risk associated with it. You could definitely brick your Surface if you do not do this properly. I am not responsible for bricked devices.
That said, here's how I did it: NOTE: You will need to use a separate Windows 8 / 8.1 /Windows Server 2012 / R2 system to do some of this work on, in addition to your Surface. There will be some work required in order to integrate the drivers and grab your Product Key.
ALSO NOTE: None of this is illegal because you will use your existing and legitimate Windows RT 8.0 Product Key to activate your copy of Windows. The key I provide for installation is just to get you through the install process. It *will not* activate.