I agree with the no, but you can make space itself rotate because things in space rotate: https://en.wikipedia.org/wiki/Frame-dragging
And that in turn would rotate things in space... or not?
What we're talking about here are closed timelike curves. There's models which suggest they could exist inside a singularity, but they're not going to outside without something which seriously breaks other areas of physics (Tipler cylinders etc).
A singularity is a dimensionless point. It has no inside. Did you mean a black hole? If so, the Kurtzgesagt cartoon explains this.
The second part of you sentence seems to have a broken sentence structure. Can't make sense of it.
...but [closed time-like curves are] not going to [exist] outside [of a singularity] without something which seriously breaks other areas of physics (Tipler cylinders etc. [are examples of such theoretical instances which would break other areas of physics]).