  Inter-band photo-excitation of electron states with the twisted photons in
GaAs, a direct band-gap bulk semiconductor, is considered theoretically.
Assuming linearity of the quantum transition amplitudes and applying
Wigner-Eckart theorem, we derive a plane-wave expansion of twisted-photon
amplitudes and obtain relative probabilities for magnetic sub-level population
of the photo-electrons in conduction band. The approach for calculating the
position dependent electron polarization, resulting from photo-absorption of
twisted light, is described for vertical transitions in the $\Gamma$ - point.
Theoretical predictions for GaAs show the interplay of spin and orbital angular
momentum of the twisted photons that alters the magnitude and the sign of
photoelectron polarization in the region near photon's phase singularity.
