Organic-inorganic halide perovskites have attracted much attention thanks to their excellent optoelectronic performances. Here, a bulk CH3NH3PbBr3 (MAPbBr3) single crystal (SC) was fabricated, whose temperature and light polarization dependence was investigated by measuring photoluminescence. The presence of obvious band tail states was unveiled when the applied temperature was reduced from room temperature to 78 K. Temperature dependence of the bandgap of the MAPbBr3 SC was found to be abnormal compared with those of traditional semiconductors due to the presence of instabilization of out-of-phase tail states. The MAPbBr3 SC revealed an anisotropy light absorption for linearly polarized light with an anisotropy ratio of 1.45, and a circular dichroism ratio of up to 9% was discovered due to the spin-orbit coupling in the band tail states, exhibiting great polarization sensitivity of the MAPbBr3 SC for the application of light sensors. These key findings shed light on the development of potential optoelectronic and spintronic applications based on large-scaled organic-inorganic perovskite SCs.