Torsional loading of elastoplastic materials leads to size effects which are not captured by classical continuum mechanics and require the use of enriched models. In this work, an analytical solution for the torsion of isotropic perfectly plastic Cosserat cylindrical bars with circular cross-section is derived in the case of generalized von Mises plasticity accounting solely for the symmetric part of the deviatoric stress tensor. The influence of the characteristic length on the microrotation, stress and strain profiles as well as torsional size effects are then investigated. In particular, a size effect proportional to the inverse of the radius of the cylinder is found for the normalized torque. A similar analysis for an extended plasticity criterion accounting for both the couple-stress tensor and the skew-symmetric part of the stress tensor is performed by means of systematic finite element simulations. These numerical experiments predict size effects which are similar to those predicted by the analytical solution. Saturation effects and limit loads are found when the couple stress tensor enters the yield function.