The Raspberry Pi already makes a pretty great computer for a webcam, but if you want to control what that Pi is looking at, you’ll need actual movement. Make has a guide to having the Pi control a camera with servomotors.
The Raspberry Pi controls the the webcam, which a user can pan, tilt and rotate remotely. Aside from the 3D printed case you’ll have to make, it’s a pretty simple project. Head over to Make for the full guide.