  We cut and paste two Banados-Teitelboim-Zanelli (BTZ) spacetimes at a throat
by the Darmois-Israel method to construct a rotating wormhole with a thin shell
filled with a barotropic fluid. The thin shell at the throat and both sides of
the throat corotate. We investigate the linear stability of the thin shell of
the rotating wormhole against radial perturbations. We show that the wormhole
becomes more and more stable the larger its angular momentum is until the
angular momentum reaches a critical value and that the behavior of a condition
for stability significantly changes when the angular momentum exceeds the
critical value. We find that the overcritical rotating wormhole has the radius
of the thin shell, which is stable regardless of the equation of state for the
barotropic fluid.
