© ESO, 2016. Aims. Our aim is to characterize the polarized continuum emission properties including intensity, polarization position angle, and polarization percentage of Sgr A∗ at ~492 GHz. This frequency, well into the submillimeter bump where the emission is supposed to become optically thin, allows us to see down to the event horizon. Hence the reported observations contain potentially vital information on black hole properties. We have compared our measurements with previous, lower frequency observations, which provides information in the time domain. Methods. We report continuum emission properties of Sgr A∗ at ~492 GHz, based on Atacama Large Millimeter Array (ALMA) observations. We measured flux densities of Sgr A∗ from the central fields of our ALMA mosaic observations. We used calibration observations of the likely unpolarized continuum emission of Titan and the observations of Ci line emission, to gauge the degree of spurious polarization. Results. The flux density of 3.6 ± 0.72 Jy which we measured during our run is consistent with extrapolations from previous, lower frequency observations. We found that the continuum emission of Sgr A∗ at ~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 can be explained by a constant polarization position angle of ~158°± 3°. The fitted polarization percentage of Sgr A∗ during our observational period is 14% ± 1.2%. The calibrator quasar J1744-3116 we observed on the same night can be fitted to Stokes I = 252 mJy, with 7.9% ± 0.9% polarization at position angle PA = 14°± 4.2°. Conclusions. 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°± 7° intrinsic polarization position angle and (-5.6 ± 0.7) × 105 rotation measure is 155+9°-8, which is consistent with our new measurement of polarization position angle within 1σ. The polarization percentage and the polarization position angle may be varying over the period of our ALMA 12 m Array observations, which demands further investigation with future polarization observations.