Ring dips are not only a great exercise, they're a great test of scapular positioning, stability, and strength. If you have to use a shrug position and are internally rotated at the humerus, you're doing it wrong.
Instead, keep your shoulder blades pulled down (think: stay tall), shoulders back a little bit, and chest out.
Remember to lean into the dip, allowing the elbows to fold back behind you. Think about pushing the rings down, rather than pushing yourself away from the rings. Also, take note of the hand position at the top and bottom of the dip.