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I don't think there is an image processing method to determine camera rotation, not a reliable one at least. Will Stwart's answer assumes you'll always have detected objects in your image and that you can always compare them between frames to determine relative camera rotation. It also assumes that this object is not moving, or else the rotation change you'd get would be of the object and not of the camera.

It wouldn't even make much sense to use image to determine rotation, since that is a task that can be completed by just adding a 100$ sensor in your setup. IMU sensors can determine rotation very robustly with a lot less error than any image processing method would. They are even used for autonomous navigation, which seems to be your goal exactly. There are many low cost solutions that are easy to integrate in a custom project.