  The canonical methods for gravitational wave detection are ground- and
space-based laser interferometry, pulsar timing, and polarization of the cosmic
microwave background. But as has been suggested by numerous investigators,
astrometry offers an additional path to gravitational wave detection.
Gravitational waves deflect light rays of extragalactic objects, creating
apparent proper motions in a quadrupolar (and higher-order modes) pattern.
Astrometry of extragalactic radio sources is sensitive to gravitational waves
with frequencies between roughly $10^{-18}$ and $10^{-8}$ Hz ($H_0$ and 1/3
yr$^{-1}$), overlapping and bridging the pulsar timing and CMB polarization
regimes. We present a methodology for astrometric gravitational wave detection
in the presence of large intrinsic uncorrelated proper motions (i.e., radio
jets). We obtain 95% confidence limits on the stochastic gravitational wave
background using 711 radio sources, $\Omega_{GW} < 0.0064$, and using 508 radio
sources combined with the first Gaia data release: $\Omega_{GW} < 0.011$. These
limits probe gravitational wave frequencies $6\times10^{-18}$ Hz $\lesssim f
\lesssim 1\times10^{-9}$ Hz. Using a WISE-Gaia catalog of 567,721 AGN, we
predict a limit expected from Gaia alone of $\Omega_{GW} < 0.0006$, which is
significantly higher than was originally forecast. Incidentally, we detect and
report on 22 new examples of optical superluminal motion with redshifts
0.13-3.89.
