Yes, absolutely. All white Xbox 360 consoles are Xbox 360 S (Slim) models (released 2010), which feature the dedicated Kinect port (orange USB‑style connector on the back) and sufficient USB power output to run the sensor without an external power supply.
If you have a white console, you have a Slim. Just plug the Kinect into the orange port on the back, run the calibration, and play.