  We apply the anisotropic resonant scattering model developed to explain the
presence of non-Zeeman circular polarization signals recently detected in the
$^{12}\mathrm{CO}\;\left(J=2\rightarrow1\right)$ and
$\left(J=1\rightarrow0\right)$ transitions in molecular clouds to Stokes $V$
spectra of SiO $v=1$ and $v=2$, $\left(J=1\rightarrow0\right)$ masers commonly
observed in evolved stars. It is found that the observed antisymmetric "S" and
symmetric "$\cup$" or "$\cap$" shaped spectral profiles naturally arise when
the maser radiation scatters off populations of foreground molecules located
outside the velocity range covered by the background maser radiation. Using
typical values for the relevant physical parameters, it is estimated that
magnetic field strengths on the order of a few times 15 mG are sufficient to
explain the observational results found in the literature.
