Does Spinning dancer has anything to do with your eyesight
For a bit of background, this test was devised by Nobuyuki Kayahara and it was originally thought that it shows the dominance of one part of the brain to the other. This was later on discarded as a misconception (reference). It is now widely believed that the clockwise - counter-clockwise rotation is a phenomenon called Bistable perception (Reference 1 and reference 2).


  Multistable perceptual phenomena are a form of perceptual phenomena in
  which there are unpredictable sequences of spontaneous subjective
  changes. While usually associated with visual perception, such
  phenomena can be found for auditory and olfactory percepts. Famous
  examples include the Necker cube, structure from motion, monocular
  rivalry and binocular rivalry, but many more visually ambiguous
  patterns are known. Since most of these images lead to an alternation
  between two mutually exclusive perceptual states, they are sometimes
  also referred to as bistable perception(reference 1 and
  reference 2).


No, the fact that you can only see her turn clockwise has not got anything to with your vision (for the record, I have never been able to see the girl go counter- clockwise myself).


  Sometimes, a person will stare at an image and it will never reverse.
  Dr. Toppino advises staring at one part of the image, such as the
  foot, and most of the time it will eventually flip. In people who
  can’t see the reversal, it may be that one underlying neural structure
  is more dominant, but once someone finally manages to see the flip, it
  will start to happen more often (reference).




This image would help you watch her rotate counter-clockwise.



Here she is spinning clockwise.