  Motivated by the connection between pole-skipping phenomena of two point
functions and four point out-of-time-order correlators, we study the
pole-skipping phenomena for rotating BTZ black holes. In particular, we
investigate the effect of rotations on the pole-skipping point for various
fields with spin $s = 1/2, 1, 2/3$, extending the previous research for $s=0,
2$. We derive an analytic full tower of the pole-skipping points of fermionic
($s=1/2$) and vector ($s=1$) fields by the exact holographic Green's functions.
For the \textit{non-extremal} black hole, the leading pole-skipping frequency
is $\omega_{\text{leading}}=2\pi i T_h {(s-1+\nu \Omega)}/{(1-\Omega^2)}$ where
$T_h$ is the temperature, $\Omega$ the rotation, and $\nu:=(\Delta_+ -
\Delta_-)/2$, the difference of conformal dimensions ($\Delta_{\pm}$). These
are confirmed by another independent method: the near-horizon analysis. For the
\textit{extremal} black hole, we find that the leading pole-skipping frequency
can occur at $\omega_{\text{leading}}^{\text{extremal}}=-2\pi i T_R {(s+1)}$
only when $\nu = s+1$, where $T_R$ is the temperature of the right moving mode.
It is non-trivial because it cannot be achieved by simply taking the extreme
limit ($T_h\rightarrow 0\,, \Omega\rightarrow 1$) of the non-extremal black
hole result.
