  The recent discovery of a weak surface magnetic field on the normal
intermediate-mass star Vega raises the question of the origin of this magnetism
in a class of stars that was not known to host magnetic fields. We aim to
confirm the field detection and provide additional observational constraints
about the field characteristics, by modelling the magnetic geometry of the star
and by investigating the seasonal variability of the reconstructed field. We
analyse a total of 799 circularly-polarized spectra collected with the NARVAL
and ESPaDOnS spectropolarimeters during 2008 and 2009. We employ a
cross-correlation procedure to compute, from each spectrum, a mean polarized
line profile with a signal-to-noise ratio of about 20,000. The technique of
Zeeman-Doppler Imaging is then used to determine the rotation period of the
star and reconstruct the large-scale magnetic geometry of Vega at two different
epochs. We confirm the detection of circularly polarized signatures in the mean
line profiles. The amplitude of the signatures is larger when spectral lines of
higher magnetic sensitivity are selected for the analysis, as expected for a
signal of magnetic origin. The short-term evolution of polarized signatures is
consistent with a rotational period of 0.732 \pm 0.008 d. The reconstructed
magnetic topology unveils a magnetic region of radial field orientation,
closely concentrated around the rotation pole. This polar feature is
accompanied by a small number of magnetic patches at lower latitudes. No
significant variability in the field structure is observed over a time span of
one year. The repeated observation of a weak photospheric magnetic field on
Vega suggests that a previously unknown type of magnetic stars exists in the
intermediate-mass domain. Vega may well be the first confirmed member of a much
larger, as yet unexplored, class of weakly-magnetic stars.
