We present a study of the magnetic field of the Large Magellanic Cloud (LMC), carried out using diffuse polarized synchrotron emission data at 1.4GHz acquired at the Parkes Radio Telescope and the Australia Telescope Compact Array. The observed diffuse polarized emission is likely to originate above the LMC disk on the near side of the galaxy. Consistent negative rotation measures (RMs) derived from the diffuse emission indicate that the line-of-sight magnetic field in the LMC's near-side halo is directed coherently away from us. In combination with RMs of extragalactic sources that lie behind the galaxy, we show that the LMC's large-scale magnetic field is likely to be of quadrupolar geometry, consistent with the prediction of dynamo theory. On smaller scales, we identify two brightly polarized filaments southeast of the LMC, associated with neutral hydrogen arms. The filaments' magnetic field potentially aligns with the direction toward the Small Magellanic Cloud (SMC). We suggest that tidal interactions between the SMC and the LMC in the past 10^9^ years are likely to have shaped the magnetic field in these filaments.