Can you use an thunderbolt cable to connect an Xbox 360 to an iMac?

No, you cannot use a Thunderbolt cable to connect an Xbox 360 to an iMac. The Xbox 360 does not support video input through Thunderbolt, and iMacs typically do not function as display devices for consoles. Instead, you would need a compatible HDMI capture card or a dedicated monitor for connecting the Xbox 360.