Stellar prominences detected in rapidly rotating stars serve as probes of the magnetism in the corona of cool stars. We have synthesized the temporal evolution of the Stokes profiles generated in the He I 10 830 and 5876 Å triplets during the rotation of a prominence around a star. The synthesis was performed with the HAZEL code using a cloud model in which the prominence is characterized by a slab located at a fixed latitude and height. It accounts for the scattering polarization and Zeeman and Hanle effects. Several cases with different prominence magnetic field strengths and orientations have been analysed. The results show an emission feature that drifts across the profile while the prominence is out of the stellar disc. When the prominence eclipses the star, the intensity profile shows an absorption. The scattering induced by the prominence generates linear polarization signals in Stokes Q and U profiles, which are modified by the Hanle effect when a magnetic field is present. Due to the Zeeman effect, Stokes V profiles show a signal with very low amplitude when the magnetic field along the line of sight is different from zero. The estimated linear polarization signals could potentially be detected with the future spectropolarimeter Mid-resolution InfRAreD Astronomical Spectrograph, to be attached to Gran Telescopio Canarias telescope.