We present a study of the magnetic field of the Small Magellanic Cloud (SMC), carried out using radio Faraday rotation and optical starlight polarization data. Consistent negative rotation measures (RMs) across the SMC indicate that the line-of-sight magnetic field is directed uniformly away from us with a strength 0.19+/-0.06{mu}G. Applying the Chandrasekhar-Fermi method to starlight polarization data yields an ordered magnetic field in the plane of the sky of strength 1.6+/-0.4uG oriented at a position angle 4+/-12{deg}, measured counterclockwise from the great circle on the sky joining the SMC to the Large Magellanic Cloud (LMC). We construct a three-dimensional magnetic field model of the SMC, under the assumption that the RMs and starlight polarization probe the same underlying large-scale field. further test the pan-Magellanic field hypothesis.