The effect of astigmatism on states of polarization of aberrant stochastic electromagnetic beams in turbulent atmosphere is investigated. Using the Gaussian-Schell model source with astigmatism, the analytical formula for the degree of polarization, the orientation angle, and the degree of polarization ellipse are derived. Analytical results show that different strengths of astigmatism have different effects on states of polarization on propagation. It is also shown that when the astigmatic coefficient of sources is large enough, states of polarization are hardly affected by atmospheric turbulence and the free-space diffraction phenomenon. The sufficient conditions for propagating with invariant polarization are derived and discussed.