We study the possibility of producing x-gamma rays with orbital angular momentum by means of the inverse Compton backscattering between a high brightness electron beam and a twisted laser pulse. We use the classical electrodynamics retarded fields for evaluating the orbital angular momentum of the radiation and connecting it to that of the primary laser pulse. We then propose the dimensioning of a linearly polarized x-ray source with orbital angular momentum, starting from the parameters of operating Thomson setups
