  Fast rotating Wolf-Rayet stars are expected to be progenitors of long
duration gamma-ray bursts. However, the observational test of this model is
problematic. Spectral lines of Wolf-Rayet stars originate in expanding stellar
wind, therefore a reliable spectroscopical determination of their rotational
velocities is difficult. Intrinsic polarization of Wolf-Rayet stars due to the
rotational modulation of the stellar wind may provide an indirect way to
determine the rotational velocities of these stars. However, detailed wind
models are required for this purpose. We determine the intrinsic polarization
of Wolf-Rayet stars from hydrodynamical wind models as a function of rotational
velocity. We used 2.5D hydrodynamical simulations to calculate the structure of
rotating winds of Wolf-Rayet stars. The simulations account for the deformation
of the stellar surface due to rotation, gravity darkening, and nonradial
forces. From the derived models, we calculated the intrinsic stellar
polarization. The mass loss rate was scaled to take realistic wind densities of
Wolf-Rayet stars into account. The hydrodynamical wind models predict a prolate
wind structure, which leads to a relatively low level of polarization. Even
relatively large rotational velocities are allowed by observational constrains.
The obtained wind structure is similiar to that obtained previously for
rotating optically thin winds. Derived upper limits of rotational velocities of
studied Wolf-Rayet stars are not in conflict with the model of long duration
gamma-ray bursts
