Godel models of the universe filled with fluid are studied in the framework of the Einstein-Cartan theory of gravitation. It is assumed that the models admit a group of motions simply transitive on space-time. The combined effects of spin and rotation(vorticity) are studied with a particular attention to whether the held equations impose any restriction on alignement of spin direction (a polarized spin distribution). The solutions are found explicitly in a closed form, which show that spin components are vanishingly small except in the direction of z-axis (the compass of inertia) in which they can assume an arbitrary distribution.