The theory of the generation and transfer of polarized radiation, mainly developed for interpreting solar spectropolarimetric observations, allows us to reconsider, in a more rigorous and elegant way, a physical mechanism that has been suggested some years ago to interpret the high degree of polarization often observed in astronomical masers. This mechanism, for which the name of ``dichroic maser'' is proposed, can operate when a low-density molecular cloud is illuminated by an anisotropic source of radiation (e.g., a nearby star). Here we investigate completely unsaturated masers and show that selective stimulated emission processes are capable of producing highly polarized maser radiation in a nonmagnetic environment. The polarization of the maser radiation is linear and is directed tangentially to a ring equidistant to the central star. We show that the Hanle effect due to the presence of a magnetic field can produce a rotation (from the tangential direction) of the polarization by more that 45° for some selected combinations of the strength, inclination, and azimuth of the magnetic field vector. However, these very same conditions produce a drastic inhibition of the maser effect. The rotations of about 90° observed in SiO masers in the evolved stars TX Cam by Kemball & Diamond and IRC +10011 by Desmurs and coworkers may then be explained by a local modification of the anisotropy of the radiation field, being transformed from mainly radial to mainly tangential.