We present the first interferometric polarization map of the W3(OH) massive star-forming region observed with the Submillimeter Array (SMA) at 878 mum with an angular resolution of 1.5 (about 3 times 10 AU). Polarization is detected in the W3(H2O) hot core, an extended emission structure in the north-west of W3(H2O), and part of the W3(OH) ultracompact HII region. The W3(H2O) hot core is known to be associated with a synchrotron jet along the east-west direction. In this core, the inferred magnetic field orientation is well aligned with the synchrotron jet and close to the plane of sky. Using the Chandrasekhar-Fermi method with the observed dispersion in polarization angle, we estimate a plane-of-sky magnetic field strength of 17.0 mG. Combined with water maser Zeeman measurements, the total magnetic field strength is estimated to be 17.1 mG, comparable to the field strength estimated from the synchrotron model. The magnetic field energy dominates over turbulence in this core. In addition, the depolarization effect is discerned in both SMA and JCMT measurements. Despite the great difference in angular resolutions and map extents, the polarization percentage shows a similar power-law dependence with the beam averaged column density. We suggest that the column density may be an important factor to consider when interpreting the depolarization effect.