We observed polarization of the SiO rotational transitions from Orion Source I (SrcI) to probe the magnetic field in bipolar outflows from this high mass protostar. Both 43 GHz $J$=1-0 and 86 GHz $J$=2-1 lines were mapped with $sim$20 AU resolution, using the Very Large Array (VLA) and Atacama Large Millimeter/Submillimeter Array (ALMA), respectively. The $^{28}$SiO transitions in the ground vibrational state are a mixture of thermal and maser emission. Comparison of the polarization position angles in the $J$=1-0 and $J$=2-1 transitions allows us to set an upper limit on possible Faraday rotation of $10^{4}$ radians m$^{-2}$, which would twist the $J$=2-1 position angles typically by less than 10 degrees. The smooth, systematic polarization structure in the outflow lobes suggests a well ordered magnetic field on scales of a few hundred AU. The uniformity of the polarization suggests a field strength of $sim$30 milli-Gauss. It is strong enough to shape the bipolar outflow and possibly lead to sub-Keplerian rotation of gas at the base of the outflow. The strikingly high fractional linear polarizations of 80-90% in the $^{28}$SiO $v$=0 masers require anisotropic pumping. We measured circular polarizations of 60% toward the strongest maser feature in the $v$=0 $J$=1-0 peak. Anisotropic resonant scattering (ARS) is likely to be responsible for this circular polarization. We also present maps of the $^{29}$SiO $v$=0 $J$=2-1 maser and several other SiO transitions at higher vibrational levels and isotopologues.
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