  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. We investigate the magnetic
activity of CoRoT-7 and use the results for a better understanding of its
impact on stellar RV variations. 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. 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. 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 < 0.01 percent 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.
