We introduce the general concept of stochastic scattering polarimetry and demonstrate that the anisotropic polarizability of a scattering object can be obtained by analyzing the statistical moments of polarimetrically measured intensity distributions. This general procedure is valid even in situations where the state of polarization of the incident field is not known. The efficiency of recovering different scattering polarizabilities is demonstrated numerically for several particular cases pertaining to both far- and near-field optics.