Spin-polarized cylinders with axial magnetic fields in Einstein-Cartan gravity are used as terrestrial and astrophysical probes to test torsion theories of gravitation. We show that a spin-polarized cylinder in teleparallel gravity cannot be constructed since the constraint of the vanishing of the full Riemann-Cartan (RC) curvature tensor leads to a vanishing spin-polarized density and therefore we are left with an unpolarized cylinder which would not be useful for our purposes since only spin-polarized test masses would be able to feel torsion. Therefore, we turn our attention to a more general type of post-Riemannian space called RC spaces where the full RC curvature does not vanish. By comparison with the experiment of Ritter et al (1993 Phys. Rev. Lett. 70 701) where a spin-polarized mass is used to test spin-dependent forces with a test mass with >10²³ spin-polarized electrons in a few cubic centimetres, we are able to compute a spin density of 10^-4 g cm^-1 s^-1 and a Cartan geometrical torsion of the order of 10^-52 cm^-1, which unfortunately is beyond the quantum-limit capability of any laboratory device. However, by considering the magnetic field along a torsion balance rotation axis we are able to compute a rotation of the torsion balance of the order of 10^-2 rad s^-1 due to an effect similar to the Einstein-de Haas effect. Deviation from the flat geometry is shown to be due to the difference between the spin-torsion polarized density and the magnetic energy which allows us to compute the necessary magnetic field to cancel the spin-torsion effects. This is of the order of 10^-2 G, and can be obtained in the laboratory. In the case of neutron stars the difference between the spin density and the magnetic fields increases considerably compared with the laboratory and deviations on the metric would be appreciable. The Lense-Thirring effect is applied to a test particle to check the metric of the spin-polarized cylinder.