A long-standing solar problem has been to measure the coronal magnetic field. We believe it determines the coronal structure and dynamics from the upper chromosphere out into the heliospheric environment. It is only recently that Zeeman splitting observations of infrared coronal emission lines have been successfully used to deduce the coronal magnetic flux density. Here we extend this technique and report first results from a novel coronal magnetometer that uses an off-axis reflecting coronagraph and optical fiber-bundle imaging spectropolarimeter. We determine the line-of-sight magnetic flux density and transverse field orientation in a two-dimensional map with a sensitivity of about 1 G with 20'' spatial resolution after 70 minutes of integration. These full-Stokes spectropolarimetric measurements of the forbidden Fe XIII 1075 nm coronal emission line reveal the line-of-sight coronal magnetic field 100'' above an active region to have a flux density of about 4 G.