You cannot use the Xbox One Kinect on Xbox 360. They are distinct hardware generations with incompatible connectors and protocols.
Released in 2010, this dedicated sensor connects to:
Kinect Adventures, Dance Central series, Kinect Sports, Child of Eden, Fruit Ninja Kinect 2.
Note: Xbox 360 Kinect is discontinued. Buy used from reputable sellers; verify the adapter is included for original consoles.