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We present the first interferometric polarization map of the W51 e1/e2 molecular cores obtained with the BIMA array at 1.3 mm wavelength with approximately 3 arcsecond resolution. The polarization angle varies smoothly across the double cores with an average position angle of 23+-5 degrees for W51 e1 and 15+-7 degrees for W51 e2. The inferred magnetic field direction is parallel to the minor axis of the double cores, which is consistent with the theoretical picture that clouds collapse along the field lines. However, the magnetic field may not determine the axis of angular momentum of these two cores as the field directions of the two cores significantly differ with the previously measured directions of rotational axes. The polarization percentage decreases toward regions with high intensity, suggesting that the dust alignment efficiency decreases toward high density regions. The field directions are highly ordered, and the small dispersion of the polarization angles implies that magnetic fields are strong ($\gtrsim$ 1 mG) and perhaps dominate turbulence in W51 e1/e2.