We develop a theory of laser beam generation of shift currents in non-centrosymmetric semiconductors. The currents originate when the excited electrons transfer between different bands or scatter inside these bands, and asymmetrically shift their centres of mass in elementary cells. Quantum kinetic equations for hot-carrier distributions and expressions for the induced currents are derived using non-equilibrium Green functions. In applications, we simplify the approach to the Boltzmann limit and use it to model laser-excited GaAs in the presence of longitudinal optical phonon scattering. The shift currents are calculated in a steady-state regime.