  We consider the propagation of slow light with an orbital angular momentum
(OAM) in a moving atomic medium. We have derived a general equation of motion
and applied it in analysing propagation of slow light with an OAM in a rotating
medium, such as a vortex lattice. We have shown that the OAM of slow light
manifests itself in a rotation of the polarisation plane of linearly polarised
light. To extract a pure rotational phase shift, we suggest to measure a
difference in the angle of the polarisation plane rotation by two consecutive
light beams with opposite OAM. The differential angle $\Delta\alpha_{\ell}$ is
proportional to the rotation frequency of the medium $\omega_{\mathrm{rot}}$
and the winding number $\ell$ of light, and is inversely proportional to the
group velocity of light. For slow light the angle $\Delta\alpha_{\ell}$ should
be large enough to be detectable. The effect can be used as a tool for
measuring the rotation frequency $\omega_{\mathrm{rot}}$ of the medium.
