  We report on the polarized light curves of the Galactic Center supermassive
black hole Sagittarius A*, obtained at millimeter wavelength with the Atacama
Large Millimeter/submillimeter Array (ALMA). The observations took place as a
part of the Event Horizon Telescope campaign. We compare the observations taken
during the low variability source state on 2017 Apr 6 and 7 with those taken
immediately after the X-ray flare on 2017 Apr 11. For the latter case, we
observe rotation of the electric vector position angle with a timescale of
$\sim 70$ min. We interpret this rotation as a signature of the equatorial
clockwise orbital motion of a hot spot embedded in a magnetic field dominated
by a dynamically important vertical component, observed at a low inclination
$\sim20^\circ$. The hot spot radiates strongly polarized synchrotron emission,
briefly dominating the linear polarization measured by ALMA in the unresolved
source. Our simple emission model captures the overall features of the
polarized light curves remarkably well. Assuming a Keplerian orbit, we find the
hot spot orbital radius to be $\sim$ 5 Schwarzschild radii. We observe hints of
a positive black hole spin, that is, a prograde hot spot motion. Accounting for
the rapidly varying rotation measure, we estimate the projected on-sky axis of
the angular momentum of the hot spot to be $\sim 60^\circ$ east of north, with
a 180$^\circ$ ambiguity. These results suggest that the accretion structure in
Sgr A* is a magnetically arrested disk rotating clockwise.
