Spin-polarized cylinders with axial magnetic fields in Einstein-Cartangravity are used as terrestrial and astrophysical probes to testtorsion theories of gravitation. We show that a spin-polarized cylinder inteleparallel gravity cannot be constructed since the constraint of thevanishing of the full Riemann-Cartan (RC) curvature tensor leads to avanishing spin-polarized density and therefore we are left with anunpolarized cylinder which would not be useful for our purposes since onlyspin-polarized test masses would be able to feel torsion. Therefore, weturn our attention to a more general type of post-Riemannian space called RCspaces where the full RC curvature does not vanish. By comparison withthe experiment of Ritter et al (1993 Phys. Rev. Lett. 70 701)where a spin-polarized mass is usedto test spin-dependent forces with a test mass with >1023spin-polarized electrons in a few cubic centimetres, we are able to computea spin density of 10-4 g cm-1 s-1 and a Cartangeometrical torsion of the order of 10-52 cm-1, whichunfortunately is beyond the quantum-limit capability of any laboratorydevice. However, by considering the magnetic field along a torsion balancerotation axis we are able to compute a rotation of the torsion balance ofthe order of 10-2 rad s-1 due to an effect similar tothe Einstein-de Haas effect. Deviation from the flat geometry is shown tobe due to the difference between the spin-torsion polarized density and themagnetic energy which allows us to compute the necessary magnetic field tocancel the spin-torsion effects. This is of the order of 10-2 G, and can be obtained in the laboratory. In the case of neutronstars the difference between the spin density and the magnetic fieldsincreases considerably compared with the laboratory and deviations on themetric would be appreciable. The Lense-Thirring effect is applied to a testparticle to check the metric of the spin-polarized cylinder.