  Stellar activity is a potential important limitation to the detection of low
mass extrasolar planets with indirect methods (RV, photometry, astrometry). In
previous papers, using the Sun as a proxy, we investigated the impact of
stellar activity (spots, plages, convection) on the detectability of an
Earth-mass planet in the habitable zone (HZ) of solar-type stars with RV
techniques. We extend here the detectability study to the case of astrometry.
We used the sunspot and plages properties recorded over one solar cycle to
infer the astrometric variations that a Sun-like star seen edge-on, 10 pc away,
would exhibit, if covered by such spots/bright structures. We compare the
signal to the one expected from the astrometric wobble (0.3 {\mu}as) of such a
star surrounded by a one Earth-mass planet in the HZ. We also briefly
investigate higher levels of activity. The activity-induced astrometric signal
along the equatorial plane has an amplitude of typ. less than 0.2 {\mu}as
(rms=0.07 {\mu}as), smaller than the one expected from an Earth-mass planet at
1 AU. Hence, for this level of activity, the detectability is governed by the
instrumental precision rather than the activity. We show that for instance a
one Earth-mass planet at 1 AU would be detected with a monthly visit during
less than 5 years and an instrumental precision of 0.8 {\mu}as. A level of
activity 5 times higher would still allow such a detection with a precision of
0.35 {\mu}as. We conclude that astrometry is an attractive approach to search
for such planets around solar type stars with most levels of stellar activity.
