Can an Xbox 360 be hooked up to a Thunderbolt display?
The Thunderbolt display expects a full Thunderbolt signal (that is, muxed PCI-Express and DisplayPort). It will not work with DisplayPort-only sources.

To date, I've not heard of any announced (let alone released) adapters that could drive a Thunderbolt display from a non-Thunderbolt source.

If you really need to do this, you might be able to hook the Xbox up to an HDMI capture card (it needs to support HDCP) that is connected to a Thunderbolt-equipped computer to which the display is connected. These capture cards are usually used by professional video editors and can be quite expensive.