Not in this game, but she may have had one in MKDA.
It should be worth noting that the real life Special Forces bear the nickname of "Green Berets" due to the distinctive headwear they are known to wear, so Sonya wearing that beret in that screenshot is most likely a reference to the real life Special Forces.
yeah she had an outfit with the beret before. I wonder why did they remove it in MKX, it's clear the model was done (and i would have prefered it miles over the camo paint)