  Binary supermassive black holes (BSBHs) are expected to be a generic
byproduct from hierarchical galaxy formation. The final coalescence of BSBHs is
thought to be the loudest gravitational wave (GW) siren, yet no confirmed BSBH
is known in the GW-dominated regime. While periodic quasars have been proposed
as BSBH candidates, the physical origin of the periodicity has been largely
uncertain. Here we report discovery of a periodicity (P=1607$\pm$7 days) at
99.95% significance (with a global p-value of ~$10^{-3}$ accounting for the
look elsewhere effect) in the optical light curves of a redshift 1.53 quasar,
SDSS J025214.67-002813.7. Combining archival Sloan Digital Sky Survey data with
new, sensitive imaging from the Dark Energy Survey, the total ~20-yr time
baseline spans ~4.6 cycles of the observed 4.4-yr (restframe 1.7-yr)
periodicity. The light curves are best fit by a bursty model predicted by
hydrodynamic simulations of circumbinary accretion disks. The periodicity is
likely caused by accretion rate modulation by a milli-parsec BSBH emitting GWs,
dynamically coupled to the circumbinary accretion disk. A bursty hydrodynamic
variability model is statistically preferred over a smooth, sinusoidal model
expected from relativistic Doppler boost, a kinematic effect proposed for
PG1302-102. Furthermore, the frequency dependence of the variability amplitudes
disfavors Doppler boost, lending independent support to the circumbinary
accretion variability hypothesis. Given our detection rate of one BSBH
candidate from circumbinary accretion variability out of 625 quasars, it
suggests that future large, sensitive synoptic surveys such as the Vera C.
Rubin Observatory Legacy Survey of Space and Time may be able to detect
hundreds to thousands of candidate BSBHs from circumbinary accretion with
direct implications for Laser Interferometer Space Antenna.
