We study the neutrino scattering off a rotating black hole with a realistic accretion disk permeated by an intrinsic magnetic field. Neutrino trajectories in curved spacetime as well as the particle spin evolution in dense matter of an accretion disk and in the magnetic field are accounted for exactly. We obtain the fluxes of outgoing ultrarelativistic neutrinos taking into account the change of the neutrino polarization owing to spin oscillations. Using the conservative value of the neutrino magnetic moment and realistic radial distributions of the matter density and the magnetic field strength, we get that these fluxes are reduced by several percent compared to the case when no spin oscillations are accounted for. In some situations, there are spikes in the neutrino fluxes because of the neutrino interaction with the rotating plasma of an accretion disk. Taking into account the uncertainties in the astrophysical neutrino fluxes, the predicted effects turn out to be quite small to be observed with the current neutrino telescopes.
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