  We report the identification of a low-mass AGN, DES J0218$-$0430, in a
redshift $z = 0.823$ galaxy in the Dark Energy Survey (DES) Supernova field. We
select DES J0218$-$0430 as an AGN candidate by characterizing its long-term
optical variability alone based on DES optical broad-band light curves spanning
over 6 years. An archival optical spectrum from the fourth phase of the Sloan
Digital Sky Survey shows both broad Mg II and broad H$\beta$ lines, confirming
its nature as a broad-line AGN. Archival XMM-Newton X-ray observations suggest
an intrinsic hard X-ray luminosity of $L_{{\rm
2-12\,keV}}\sim7.6\pm0.4\times10^{43}$ erg s$^{-1}$, which exceeds those of the
most X-ray luminous starburst galaxies, in support of an AGN driving the
optical variability. Based on the broad H$\beta$ from SDSS spectrum, we
estimate a virial BH mass of $M_{\bullet}\approx10^{6.43}$-$10^{6.72}M_{\odot}$
(with the error denoting 1$\sigma$ statistical uncertainties only), consistent
with the estimation from OzDES, making it the lowest mass AGN with redshift $>$
0.4 detected in optical. We estimate the host galaxy stellar mass to be
$M_{\ast}\sim10^{10.5\pm0.3}M_{\odot}$ based on modeling the multi-wavelength
spectral energy distribution. DES J0218$-$0430 extends the
$M_{\bullet}$-$M_{\ast}$ relation observed in luminous AGNs at $z\sim1$ to
masses lower than being probed by previous work. Our work demonstrates the
feasibility of using optical variability to identify low-mass AGNs at higher
redshift in deeper synoptic surveys with direct implications for the upcoming
Legacy Survey of Space and Time at Vera C. Rubin Observatory.
