Given the context you gave (dark circles), I would use "on" although I would expect to see dark circles around her eyes, not on her face. Are we talking about the normal dark circles around the eyes?
She sees dark circles around Anne's eyes.
She sees dark circles on Anne's face.
We use "in" and "on" when talking about signs of an emotion.
I could see it in her face - she was devastated.
Her confusion was obvious on her face.
(Her confusion was written all over her face.)
Student or Learner