We use first first-principle methods and the Peierls-Nabarro model to evaluate the resistance to glide, characterized by the Peierls stress, of glide systems for end-member MgSiO3 Perovskite at mantle pressures. [010](100) is the easiest glide system in Mg-Perovskite at all pressures. Peierls stresses increase systematically with pressure for all systems except [001](010), indicating the importance of lattice friction at lower mantle pressures. The ratio of the maximum Peierls stress for each system relative to the [010](100) value defines their critical resolved shear stress (CRSS). These CRSS are used in a visco-plastic self-consistent homogenization model to predict the evolution of crystal preferred orientations (CPO) during deformation of polycrystalline Mg-Perovskite. In axial compression, [100] tends to align with the compression direction, in agreement with in situ observations in axial compression experiments. In simple shear, [010] concentrates near the shear direction and (100), although more dispersed, tends to align near the shear plane, consistent with the dominant activity of the easier [010](100) system. The calculated seismic anisotropy for a 100% Mg-Perovskite aggregate using the CPO in simple shear and the elastic constants Of MgSiO3 perovskite at lower mantle pressures and temperatures is weak (>3% for P-waves with and >2% for S-waves) and decreases with increasing temperature and pressure. P-waves show the fastest propagation parallel to the lineation and S-waves fast polarization is in the foliation at 38 GPa and normal to the lineation at 88 GPa. This weak anisotropy is consistent with global seismological observations of a nearly isotropic lower mantle. There are however two regions where strain-induced Mg-Perovskite CPO could contribute to anisotropy; a) low temperature regions in the uppermost lower mantle, where the predicted S-wave polarization anisotropy may attain 1.6% with a fast polarization parallel to the foliation, b) in high high-temperature domains in the D '' layer, where Mg-Perovskite may be the major stable phase, leading to polarization of fast S-waves normal to the lineation for propagation directions at high angle to the lineation and an apparent isotropy for all other propagation directions.