A theory is presented for the development of circular polarization as radio waves propagate through the turbulent, birefringent interstellar medium. The fourth order moments of the wave field are calculated, and it is shown that unpolarized incident radiation develops a nonzero variance in circular polarization. A magnetized turbulent medium causes the Stokes parameters to scintillate in a nonidentical manner. A specific model for this effect is developed for the case of density fluctuations in a uniform magnetic field.