  Context. Gaia Early Data Release 3 (Gaia EDR3) provides accurate astrometry
for about 1.6 million compact (QSO-like) extragalactic sources, 1.2 million of
which have the best-quality five-parameter astrometric solutions.
  Aims. The proper motions of QSO-like sources are used to reveal a systematic
pattern due to the acceleration of the solar system barycentre with respect to
the rest frame of the Universe. Apart from being an important scientific result
by itself, the acceleration measured in this way is a good quality indicator of
the Gaia astrometric solution. Methods. The effect of the acceleration is
obtained as a part of the general expansion of the vector field of proper
motions in Vector Spherical Harmonics (VSH). Various versions of the VSH fit
and various subsets of the sources are tried and compared to get the most
consistent result and a realistic estimate of its uncertainty. Additional tests
with the Gaia astrometric solution are used to get a better idea on possible
systematic errors in the estimate.
  Results. Our best estimate of the acceleration based on Gaia EDR3 is $(2.32
\pm 0.16) \times 10^{-10}$ m s${}^{-2}$ (or $7.33 \pm 0.51$ km s$^{-1}$
Myr${}^{-1}$) towards $\alpha = 269.1^\circ \pm 5.4^\circ$, $\delta =
-31.6^\circ \pm 4.1^\circ$, corresponding to a proper motion amplitude of $5.05
\pm 0.35$ $\mu$as yr${}^{-1}$. This is in good agreement with the acceleration
expected from current models of the Galactic gravitational potential. We expect
that future Gaia data releases will provide estimates of the acceleration with
uncertainties substantially below 0.1 $\mu$as yr${}^{-1}$.
