DIAGNOSIS That's the internal infrared (IR) LED cut filter physically moving to switch between day and night mode. On some units, the mechanism is audible, especially in a quiet environment.
FIX If it's constant, the filter might be stuck mid-shift. Try covering the camera lens with your hand for 30 seconds to force night mode (IR on), then uncover it to go back to day mode. This cycle can sometimes unstick it. Also, make sure the camera firmware is updated in the Ring app, as updates have addressed noise issues in the past.
IF THAT DIDN'T WORK The noise could be coming from the power supply (transformer) if it's faulty or low-quality, not the camera itself. Try a different compatible power supply (16-24V AC, min 20VA) if you have one, or contact Ring support—a persistent mechanical buzz from the camera itself is often considered a hardware defect.
HEADS UP A faint click during the day/night transition is normal. A continuous buzz or whine is not. If it's under warranty, Ring will usually replace a unit with a defective filter mechanism.