  Gravitational wave (GW) detections have enriched our understanding of the
universe. To date, all single-source GW events were found by
interferometer-type detectors. We study a detection method using astrometric
solutions from photometric surveys and demonstrate that it offers a highly
flexible frequency range, uniquely complementing existing detection methods.
From repeated point-source astrometric measurements, we may extract GW-induced
deflections and infer wave parameters. This method can be applied to any
photometric surveys measuring relative astrometry. We show that high-cadence
observations of the galactic bulge, such as offered by the Roman Space
Telescope's Exoplanet MicroLensing (EML) survey, can be a potent GW probe with
complementary frequency range to Gaia, pulsar timing arrays (PTAs), and the
Laser Interferometer Space Antenna (LISA). We calculate that the Roman EML
survey is sensitive to GWs with frequencies ranging from $7.7\times10^{-8}$Hz
to $5.6\times10^{-4}$Hz, which opens up a unique GW observing window for
supermassive black hole binaries and their waveform evolution. While the
detection threshold assuming the currently expected performance proves too high
for detecting individual GWs in light of the expected supermassive black hole
binary population distribution, we show that binaries with chirp mass
$M_c>10^{8.3}~M_\odot$ out to 100 Mpc can be detected if the telescope is able
to achieve an astrometric accuracy of 0.11 mas. To confidently detect binaries
with $M_c>10^{7}~M_\odot$ out to 50 Mpc, a factor of 100 sensitivity
improvement is required. We propose several improvement strategies, including
recovering the mean astrometric deflection and increasing astrometric accuracy,
number of observed stars, field-of-view size, and observational cadence. We
discuss how other existing and planned photometric surveys could contribute to
detecting GWs via astrometry.
