The linear magneto-optical absorption of a polaron is derived for the Faraday (active and inactive mode) and the Voigt configurations. Our calculation is intended to be valid for arbitrary electron-phonon coupling constant, temperature, and magnetic fields. We start from the Kubo formula for the frequency-dependent conductivity and show that the essential quantity which we have to calculate is the electron density-density correlation function. This function is obtained by using the anisotropic Feynman polaron model. At zero magnetic field our result reduces to the optical absorption corresponding to the Feynman-Hellwarth-Iddings-Platzman approximation for a Fröhlich polaron, as derived by Devreese et al. [Phys. Rev. B 5, 2367 (1972)]. For small electron-phonon coupling the perturbation result is reobtained. Special attention is paid to the effect of the polaron instability [F.M. Peeters and J. T. Devreese, Phys. Rev. B 25, 7302 (1982)] on the magneto-optical absorption spectrum.