  The structure function approach and the parton picture, developed for the
theoretical description of the deep inelastic electron-proton scattering, also
proved to be very effective for calculation of radiative corrections in Quantum
Electrodynamics. We use them to calculate radiative corrections to the cross
section of electron-proton scattering due to electron-photon interaction, in
the experimental setup with the recoil proton detection, proposed by A.A.
Vorobev to measure the proton radius. In the one-loop approximation, explicit
expressions for these corrections are obtained for arbitrary momentum
transfers. It is shown that, at momentum transfers small compared with the
proton mass, various contributions to the corrections mutually cancel each
other with power accuracy. In two loops, the corrections are obtained in the
leading logarithmic approximation.
