We calculate the processes π^±γ→π^±γ^* and π^±γ→^±γ^*, using a model based on QCD. From the first one, we derive the cross section of the Compton effect π^±γ→π^±γ. Considering an experiment where the above processes can be measured via the Primakoff effect, we notice that an appreciable yield may be obtained, at least for the reaction π^±N→π^±γN.