  We demonstrate the optical orientation and alignment of excitons in a
two-dimensional layer of CsPbI$_3$ perovskite nanocrystals prepared by
colloidal synthesis and measure the anisotropic exchange splitting of exciton
levels in the nanocrystals. From the experimental data at low temperature (2K),
we obtain the average value of anisotropic splitting of bright exciton states
of the order of 120{\mu}eV. Our calculations demonstrate that there is a
significant contribution to the splitting due to the nanocrystal shape
anisotropy for all inorganic perovskite nanocrystrals.
