We present an investigation into the magnetism of the Magellanic Bridge, carried out through the observation of Faraday rotation towards 167 polarized extragalactic radio sources spanning the continuous frequency range of 1.3 - 3.1 GHz with the Australia Telescope Compact Array. Comparing measured Faraday depth values of sources 'on' and 'off' the Bridge, we find that the two populations are implicitly different. Assuming that this difference in populations is due to a coherent field in the Magellanic Bridge, the observed Faraday depths indicate a median line-of-sight coherent magnetic-field strength of $B_{∥}\,≃\,0.3\,μ$G directed uniformly away from us. Motivated by the varying magnitude of Faraday depths of sources on the Bridge, we speculate that the coherent field observed in the Bridge is a consequence of the coherent magnetic fields from the Large and Small Magellanic Clouds being pulled into the tidal feature. This is the first observation of a coherent magnetic field spanning the entirety of the Magellanic Bridge and we argue that this is a direct probe of a 'pan-Magellanic' field. ; Comment: 21 pages, 11 figures