We report linearly polarized continuum emission properties of Sgr A* at $sim$492 GHz, based on the Atacama Large Millimeter Array (ALMA) observations. We used the observations of the likely unpolarized continuum emission of Titan, and the observations of Ctextsc{i} line emission, to gauge the degree of spurious polarization. The Stokes I flux of 3.6$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.
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