I've been running the 8.1 Preview on my Windows RT device since it was available. It was a nice improvement. Yesterday the RTM version of 8.1 was available, and I wanted to get it on my Surface RT running Windows RT. I checked Windows Update and it wasn't an option. I checked the Store, and I was seeing some odd behavior. I couldn't' find it via search, although I wasn't 100% of the title of what I was looking for. I did some digging, and it turns out there's an easy way to do the upgrade. Open a browser and type in "ms-windows-store:WindowsUpgrade" (without the quotes). This will open a link to the Upgrade in the Windows Store. From there I clicked the install button and let it do it's magic. I'm now running Windows 8.1 RTM on my Surface RT.
Warning: The store just showed the spinning dotted circle for a while after clicking install. The machine was installing the update during this time. You can bring up the task manager to see if the machine is working. Press Ctrl-Shift-Escape to bring it up. Hit the more details arrow. Then switch to the performance tab. You should see CPU activity. Mine stayed above 20% the whole time and spiked higher.
UPDATE: It appears that the 8.1 preview has been temporarily pulled. If this method doesn't work, the update is likely not back yet.