Can Kalman Filter be used to track Randomly Moving Target?
It depends on what you mean by a "randomly moving object".  If you are trying to track something that truly moves around in a totally uncorrelated manner from sample to sample (like, say, a laser pointer that flickers on and off and randomly changes position in your camera images) then a linear tracker will not give you insight into the object's state.  

The examples you cited (a moving hand, bird, etc.) might exhibit random behavior on "large" time scales, but on "small" time scales their state is highly correlated. For such a system the most important point is to have a high data sampling rate relative to the dynamics of the system.  The higher the sampling and measurement update rate, the more linear the underlying system dynamics will be from one measurement time to the next.  Also if you know the object of interest can be randomly changing direction or accelerating you can incorporate this prior knowledge by increasing the process noise during the prediction phase of your Kalman filter, giving less weight to the predicted position during the "update" stage.