Spectro-polarimetric signatures of accretion disks in X-ray binaries and active galactic nuclei contain information on the masses and spins of their central black holes, as well as the geometry of matter in proximity to the compact objects. This information can be extracted by means of X-ray polarimetry. In this work, we present a fast analytical ray-tracing technique for polarized light (artpol) that helps us to obtain the spinning black hole parameters from the observed properties. This technique can replace the otherwise time-consuming numerical ray-tracing calculations for any optically thick or geometrically thin accretion flow. For the purposes of illustration, we considered a standard optically thick, geometrically thin accretion disk in the equatorial plane of the Kerr black hole. We show that artpol proves accurate for dimensionless spin parameter a ≤ 0.94 with a speed that is over four orders of magnitude faster than direct ray-tracing calculations. This approach opens up broader prospects for direct fittings of the spectro-polarimetric data from the Imaging X-ray Polarimetry Explorer.