Not that I'm aware of because it runs Windows 8 RT so iTunes would have to create an app in order to run it on this surface. However, if you were to wait for the Surface Pro to be released, it runs the full version of Windows 8 and would be able to run iTunes.
No you can not download iTunes to the Surface RT. Like you I wish I had known that before purchasing. As a matter of fact, I should have researched a little more, there are many apps that are not available for the Surface RT.