If your shoulders are tight in the golf swing, it will limit not only your shoulder rotation, but also your rotation in your torso causing an abbreviated backswing or limited weight shift.

Standing in upright posture, place your arm around an exercise ball (if you do not have an exercise ball, you can just hold your arm up in the air).
Keep your shoulders relaxed and gaze forward.
Rotate your head away from your raised arm. Hold position for a moment and return to start position. Keep your shoulder down as you turn your head away from your raised arm.
Repeat motion on opposite side.