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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 motionand applied it in analysing propagation of slow light with an OAM in a rotatingmedium, such as a vortex lattice. We have shown that the OAM of slow lightmanifests itself in a rotation of the polarisation plane of linearly polarisedlight. To extract a pure rotational phase shift, we suggest to measure adifference in the angle of the polarisation plane rotation by two consecutivelight beams with opposite OAM. The differential angle $\Delta\alpha_{\ell}$ isproportional to the rotation frequency of the medium $\omega_{\mathrm{rot}}$and the winding number $\ell$ of light, and is inversely proportional to thegroup velocity of light. For slow light the angle $\Delta\alpha_{\ell}$ shouldbe large enough to be detectable. The effect can be used as a tool formeasuring the rotation frequency $\omega_{\mathrm{rot}}$ of the medium.

Polarisation rotation of slow light with orbital angular momentum in ultracold atomic gases