  We use high resolution numerical simulations to study whether gravitational
instabilities within circumstellar discs can produce astrometrically detectable
motion of the central star. For discs with masses of M_disc = 0.1 M_star, which
are permanantly stable against fragmentation, we find that the magnitude of the
astrometric signal depends upon the efficiency of disc cooling. Short cooling
times produce prominent filamentary spiral structures in the disc, and lead to
stellar motions that are potentially observable with future high precision
astrometric experiments. For a disc that is marginally unstable within radii of
\~10 au, we estimate astrometric displacements of 10-100 microarcsec on decade
timescales for a star at a distance of 100 pc. The predicted displacement is
suppressed by a factor of several in more stable discs in which the cooling
time exceeds the local dynamical time by an order of magnitude. We find that
the largest contribution comes from material in the outer regions of the disc
and hence, in the most pessimistic scenario, the stellar motions caused by the
disc could confuse astrometric searches for low mass planets orbiting at large
radii. They are, however, unlikely to present any complications in searches for
embedded planets orbiting at small radii, relative to the disc size, or Jupiter
mass planets or greater orbiting at large radii.
