Rotational Fresnel drag - or orbital Faraday rotation - in a rotating magnetised plasma is uncovered and studied analytically for Trivelpiece-Gould and Whistler-Helicon waves carrying orbital angular momentum (OAM). Plasma rotation is shown to introduce a non-zero phase shift between OAM-carrying eigenmodes with opposite helicities, similarly to the phase-shift between spin angular momentum eigenmodes associated with the classical Faraday effect in a magnetised plasma at rest. By examining the dispersion relation for these two low-frequency modes in a Brillouin rotating plasma, this Faraday-Fresnel rotation effect is traced back to the combined effects of Doppler shift, centrifugal forces and Coriolis forces. In addition, rotation is further shown to lead to rotation- and azimuthal mode-dependent longitudinal group velocity, therefore predicting the Faraday-Fresnel splitting of the enveloppe of a wave packet containing a superposition of OAM-carrying eigenmodes with opposite helicities.
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