  We report linearly polarized continuum emission properties of Sgr A* at
$\sim$492 GHz, based on the Atacama Large Millimeter Array (ALMA) observations.
We used the observations of the likely unpolarized continuum emission of Titan,
and the observations of C\textsc{i} line emission, to gauge the degree of
spurious polarization. The Stokes I flux of 3.6$\pm$0.72 Jy during our run is
consistent with extrapolations from the previous, lower frequency observations.
We found that the continuum emission of Sgr A* at $\sim$492 GHz shows large
amplitude differences between the XX and the YY correlations. The observed
intensity ratio between the XX and YY correlations as a function of parallactic
angle may be explained by a constant polarization position angle of
$\sim$158$^{\circ}$$\pm$3$^{\circ}$. The fitted polarization percentage of Sgr
A* during our observational period is 14\%$\pm$1.2\%. The calibrator quasar
J1744-3116 we observed at the same night can be fitted to Stokes I = 252 mJy,
with 7.9\%$\pm$0.9\% polarization in position angle P.A. =
4.1$^{\circ}$$\pm$4.2$^{\circ}$. The observed polarization percentage and
polarization position angle in the present work appear consistent with those
expected from longer wavelength observations in the period of 1999-2005. In
particular, the polarization position angle at 492 GHz, expected from the
previously fitted 167$^{\circ}$$\pm$7$^{\circ}$ intrinsic polarization position
angle and (-5.6$\pm$0.7)$\times$10$^{5}$ rotation measure, is 155$^{+9}_{-8}$,
which is consistent with our new measurement of polarization position angle
within 1$\sigma$. The polarization percentage and the polarization position
angle may be varying over the period of our ALMA 12m Array observations, which
demands further investigation with future polarization observations.
