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 μG. Applying the Chandrasekhar-Fermi method to starlight polarization data yields an ordered magnetic field in the plane of the sky of strength 1.6 ± 0.4 μG oriented at a position angle 4˚ ± 12˚ , 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. The vector defining the overall orientation of the SMC magnetic field shows a potential alignment with the vector joining the center of the SMC to the center of the LMC, suggesting the possibility of a "pan-Magellanic" magnetic field. A cosmic-ray-driven dynamo is the most viable explanation of the observed field geometry, but has difficulties accounting for the observed unidirectional field lines. A study of Faraday rotation through the Magellanic Bridge is needed to further test the pan-Magellanic field hypothesis.