I've always loved these animations.  I've got a few (including the traditional girl one).
 

 
Of course, the answer to the question posed in the topic is... No.
 
But your brain will spin it one way or the other.  I can now change it from spinning one way to the other easily, in fact, I can even make da kitteh bounce from left to right and back again.  Fun stuff! 

Only Schrödinger knows for sure

Perhaps a better way to describe the rotation might be clockwise or anticlockwise. (from the top looking down on the cat)
 
For me it is always one way and that is clockwise. They say the people who use the creative side of their brains will see it one way only.  I must be very creative.

I'm so creative I don't see an image spinning. 

I see pixels turning off and on.
 

BobF
Only Schrödinger knows for sure

NOT a cat lover was he?

I am incapable of seeing it spin any other way but anti-clockwise. Any other direction is hocus pocus as far as I'm concerned. 

Did Strummy hang that cat up there?

Its cool. It is spinning anti clockwise for me now! An interesting thing to do is to look at something else eg the Cakewalk logo at the top of the page and keep the cat just in indirect sight. It will change direction. And also change direction mid stream too once you look back at it.

Fascinating. Mostly clockwise for me, some accidental spins counter-clockwise.