  Angular momentum coupling between a rotating magnetized plasma and torsional
Alfv\'en waves carrying orbital angular momentum (OAM) is examined. It is not
only demonstrated that rotation is the source of Fresnel-Faraday rotation - or
orbital Faraday rotation effects - for OAM carrying Alfv\'en waves, but also
that angular momentum from an OAM carrying Alfv\'en wave can be transferred to
a rotating plasma through the inverse process. For the direct process, the
transverse structure angular rotation frequency is derived by considering the
dispersion relation for modes with opposite OAM content. For the inverse
process, the torque exerted on the plasma is derived as a function of wave and
plasma parameters.
