Google hits many results for both "Turn to the right/left" and "Turn right/left".

I wonder which one is correct grammatically.
Both are fine, as Ed says, but if you tell me to turn to the left, I may stand in place, but rotate my body.

A: I can't find my glasses.
B: They're right there, next to you.
A: Where?
B: For heaven's sake. Turn to your left. Good. Now look at the table right in front of you. Yes, there.

If I am driving/walking, and you say "turn left" I will change the direction I am travelling.

Of course, if I'm driving and you say "turn to the left" I won't look out the side window but continue to drive straight forward -- but I will wonder just a bit why didn't just say "Turn left."
I think you'll find the phrases are used interchangeably,
with little cause for preference being given one or the other,
other than the event of being in a hurry.
 BarbaraPA's reply was promoted to an answer.