As always, the real answer is that we don't know. We have no way of conducting the experiment. There are arguments both ways. So, we don't know.
The argument in favour of centripetal force is that things moving around in circles in not a natural movement and you need to use a force to make it happen.
The argument against is that it seems reasonable to assume that the universe as a whole cannot have an angular momentum (momentum of rotation). If you are the only object in the universe, then you cannot have angular momentum, cannot rotate. So, no force.
Here, the question has chanced a bit and become "If you are the only being in the universe, is it possible for you to rotate?"
This might seem like a different question, but they are connected by the definition of "rotate".
Ponder this: If you were the only object in the universe, how would you know if you were rotating?
And the answer is: "If you need a force to keep your arms and legs in place." With no remote "fixed" stars, this is the only way know if you are rotating.
This gives us two alternatives:
- There is no force. Which means there is no rotation. OR,
- There is a force. Which means that rotation is possible.
Since we can't do experiments, we can't tell which of these would be the case.
Adding another person to the universe, regardless how far away, changes everything. Now the two of you can have opposite angular momenta so that the total momentum of the universe is zero.
And you can measure you momentum by looking at the other person.