When doing warm-ups
Do we turn our head around or spin?
For exercise, "doing head rolls" is fine. It is a specific kind of warm-up exercise. You could even call it a technical word in that it wouldn't be used outside that context.
In other contexts, like when your back is toward the door and someone knocks, you would just say, "I turned my head toward the door." Saying "I turned my head around" implies 180º of motion which you don't have unless you are an owl. Or unless you are going from left to right or vice-versa.
And to say your head is spinning is an expression for when you are dizzy or very confused or overwhelmed. Literally it would mean that you head is twisting, 360º, 720º, etc.