Context : The CoRoT satellite has recently discovered the transits of a telluric planet across the disc of a late-type magnetically active star dubbed CoRoT-7 , while a second planet has been detected after filtering out the radial velocity ( hereafter RV ) variations due to stellar activity . Aims : We investigate the magnetic activity of CoRoT-7 and use the results for a better understanding of the impact of magnetic activity on stellar RV variations . Methods : We derive the longitudinal distribution of active regions on CoRoT-7 from a maximum entropy spot model of the CoRoT light curve . Assuming that each active region consists of dark spots and bright faculae in a fixed proportion , we synthesize the expected RV variations . Results : Active regions are mainly located at three active longitudes which appear to migrate at different rates , probably as a consequence of surface differential rotation , for which a lower limit of \Delta \Omega / \Omega = 0.058 \pm 0.017 is found . The synthesized activity-induced RV variations reproduce the amplitude of the observed RV curve and are used to study the impact of stellar activity on planetary detection . Conclusions : In spite of the non-simultaneous CoRoT and HARPS observations , our study confirms the validity of the method previously adopted to filter out RV variations induced by stellar activity . We find a false-alarm probability < 10 ^ { -4 } that the RV oscillations attributed to CoRoT-7b and CoRoT-7c are spurious effects of noise and activity . Additionally , our model suggests that other periodicities found in the observed RV curve of CoRoT-7 could be explained by active regions whose visibility is modulated by a differential stellar rotation with periods ranging from 23.6 to 27.6 days .