We present electrical resistivity models of the crust and upper mantle from two‐dimensional (2‐D) inversion of magnetotelluric (MT) data collected in the Rio Grande rift, New Mexico, USA. Previous geophysical studies of the lithosphere beneath the rift identified a low‐velocity zone several hundred kilometers wide, suggesting that the upper mantle is characterized by a very broad zone of modified lithosphere. In contrast, the surface expression of the rift (e.g., high‐angle normal faults and synrift sedimentary units) is confined to a narrow region a few tens of kilometers wide about the rift axis. MT data are uniquely suited to probing the depths of the lithosphere that fill the gap between surface geology and body wave seismic tomography, namely the middle to lower crust and uppermost mantle. We model the electrical resistivity structure of the lithosphere along two east‐west trending profiles straddling the rift axis at the latitudes of 36.2 and 32.0°N. We present results from both isotropic and anisotropic 2‐D inversions of MT data along these profiles, with a strong preference for the latter in our interpretation. A key feature of the anisotropic resistivity modeling is a broad (~200‐km wide) zone of enhanced conductivity (<20 Ωm) in the middle to lower crust imaged beneath both profiles. We attribute this lower crustal conductor to the accumulation of free saline fluids and partial melt, a direct result of magmatic activity along the rift. High‐conductivity anomalies in the midcrust and upper mantle are interpreted as fault zone alteration and partial melt, respectively.