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If you are trying to estabilize the video, there is a stabilization module in OpenCV. You can check that out. But if is not related to that, and you want a measure of the shakyness of the camera, you could do something like:

1. Find and compute Features in consecutive frames.
2. Match those features for every pair of consecutive frames.
3. Cross-validate and eliminate bad matches.
4. Find a Homography transformation between the features in one frame to the ones of the second frame, and reject outliers with RANSAC to achieve robustness for moving objects and matching errors.
5. You can verify the rotation angle of the camera or maybe compute the magnitude of the rotation part of the homography matrix as a shakyness strength measure.

Every step has an OpenCV method, except for step 3 I think. But you can cross validate by yourself.