We calculate the circular dichroism (CD) for absorption of the twisted photons, or optical vortices, by atoms, caused by atomic excitation into discrete energy levels. The effects of photon spin on the rates and cross sections of atomic photo-excitation are considered. It is demonstrated that although for electric dipole transitions the atomic excitation rates depend on the relative orientation of photon spin and orbital angular momentum (OAM), the resulting CD is zero. However, CD is nonzero for atomic transitions of higher multipolarity, peaking in the optical vortex center, resulting in preferred absorption of the photons with their spins aligned with OAM. The effects remain large in a paraxial limit, where analytic expressions are provided. The predicted spin asymmetries are equivalent to OAM dichroism for the fixed photon spin.
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