  Astrometric surveys can be used to constrain the stochastic gravitational
wave background (SGWB) at very low frequencies. We use proper motion data
provided by Gaia DR3 to fit a generic dipole+quadrupole field. We analyse
several quasar-based datasets and discuss their purity and idoneity to set
constraints on gravitational waves. For the cleanest dataset, we derive an
upper bound on the (frequency-integrated) energy density of the SGWB
$h_{70}^2\Omega_{\rm GW}\lesssim 0.087$ for $4.2\times
10^{-18}~\mathrm{Hz}\lesssim f\lesssim 1.1\times 10^{-8}~\mathrm{Hz}$. We also
reanalyse previous VLBI-based data to set the constraint $h_{70}^2\Omega_{\rm
GW}\lesssim 0.024$ for $5.8\times 10^{-18}~\mathrm{Hz}\lesssim f\lesssim
1.4\times 10^{-9}~\mathrm{Hz}$ under the same formalism, standing as the best
astrometric constraint on GWs. Based on our results, we discuss the potential
of future Gaia data releases to impose tighter constraints.
