We present radiative transfer calculations showing the polarization effects of scattering and absorption by aligned grains. The grain model consists of a size distribution of oblate or spinning prolate particles with varying degrees of alignment. To develop an understanding of the radiative transfer effects, we begin with the simple case of a spherical envelope illuminated by a central source with constant grain alignment axis throughout the envelope. Nonaligned grains produce no net polarization in such envelopes, while aligned grains produce substantial linear and circular polarization. The linear polarization results from the competing effects of differential extinction and scattering. The polarization varies strongly with optical depth, with scattering dominating at low optical depth and differential extinction dominating at high optical depth. The net, or integrated, circular polarization from the envelopes is zero; however, the circular polarization across the resolved nebula is large, reaching ±50% in the "diagonal" regions of the nebula. Next we calculate axisymmetric models of protostellar envelopes, again with the simplifying case of constant grain alignment axis throughout the envelope. The polarization maps show differences from the case of nonaligned grains, especially in the disk midplane, where differential extinction of even the scattered light causes the polarization vectors to align perpendicular to the disk plane, in contrast to many observations. This suggests either that grains are not aligned in protostellar envelopes or that the magnetic field (the presumed alignment mechanism) is not aligned along the disk rotational axis throughout the envelope and disk. A definitive test of grain alignment could come from resolved circular polarization maps of protostars. Aligned grains produce large values of circular polarization across the cloud, up to ±25%-40% in the models presented here, whereas nonaligned grains produce maximum polarizations of less than 1%. In objects with aligned grains, analysis of linear and circular polarization maps can probe magnetic geometries.