This paper analyses fourth-order moments of polarized radiation passing through magnetoactive plasma with random irregularities both in electron density and magnetic field. We consider the new propagation effect arising from chiral properties of random magnetoplasma. That is, the lenses formed by the same irregularities of magnetic field may be characterized by refractive properties of opposite sense vis-a-vis the rotation of wave polarization vector. This produces an appearance of slight circular polarization fluctuations arising from initially nonpolarised radiation. Analysis of the polarized radiation fluctuations may allow the spatial spectrum of magnetic field irregularities to be detected. The enchanced level of circularly polarized component, and the share of fluctuations owing to magnetic field irregularities, can be readily observed at low frequencies only, say in the radiation passing through the solar chromosphere or Jovian and terrestrial ionosphere (magnitosphere).