We use Atacama Large Millimeter/submillimeter Array Band 5 science verification observations of the red supergiant VY CMa to study the polarization of SiO thermal/masers lines and dust continuum at ~1.7 mm wavelength. We analyse both linear and circular polarization and derive the magnetic field strength and structure, assuming the polarization of the lines originates from the Zeeman effect, and that of the dust originates from aligned dust grains. We also discuss other effects that could give rise to the observed polarization. We detect, for the first time, significant polarization (~3%) of the circumstellar dust emission at millimeter wavelengths. The polarization is uniform with an electric vector position angle of $sim8^circ$. Varying levels of linear polarization are detected for the J=4-3 28SiO v=0, 1, 2, and 29SiO v=0, 1 lines, with the strongest polarization fraction of ~30% found for the 29SiO v=1 maser. The linear polarization vectors rotate with velocity, consistent with earlier observations. We also find significant (up to ~1%) circular polarization in several lines, consistent with previous measurements. We conclude that the detection is robust against calibration and regular instrumental errors, although we cannot yet fully rule out non-standard instrumental effects. Emission from magnetically aligned grains is the most likely origin of the observed continuum polarization. This implies that the dust is embedded in a magnetic field >13 mG. The maser line polarization traces the magnetic field structure. The magnetic field in the gas and dust is consistent with an approximately toroidal field configuration, but only higher angular resolution observations will be able to reveal more detailed field structure. If the circular polarization is due to Zeeman splitting, it indicates a magnetic field strength of ~1-3 Gauss, consistent with previous maser observations.
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