  The chiral optical absorption by a single vortex in a p_x \pm i p_y-wave
superconductor is studied theoretically. The p_x \pm i p_y-wave state was
recently suggested as the symmetry of the order parameter of Sr_2 Ru O_4
superconductor. Due to the violation of time reversal symmetry, there are two
types of vortices whose winding orientation is the same or opposite to the
angular momentum of the Cooper pair. In a real material domains with p_x \pm i
p_y-wave states are expected. However, optical absorption of circular polarized
light depends only on the winding of the vortex and has a low energy absorption
peak which results in dichroism. Dichroism occurs if superconductivity is
realized on a single Fermi surface sheet. However, in the case of several Fermi
surface sheets dichroism may disappear, if the both types of carriers are
present, electron-like and hole-like. Therefore chiral optical absorption is a
possible experiment to detect the orbital dependent superconductivity which was
suggested as the superconducting state of Sr_2 Ru O_4.
