The utility of Faraday rotation to measure the magnetic field of the solar corona and large-scale transients within is a small, yet growing field in solar physics. This is largely because it has been recognized as a potentially valuable frontier in space weather studies, because the ability to measure the intrinsic magnetic field within coronal mass ejections (CMEs) when they are close to the Sun is of great interest for understanding a key element of space weather. Such measurements have been attempted over the last few decades using radio signals from artificial sources (I.e., spacecraft on the far side of the Sun), but studies involving natural radio sources are scarce in the literature. We report on a preliminary study involving an attempt to detect the Faraday rotation of a CME that passed in front of a pulsar (PSR B0950+08) in 2015 August. We combine radio measurements with those from a broadband visible light coronagraph, to estimate the upper limit of the magnetic field of the CME when it was in the corona. We find agreement between different approaches for obtaining its density, and values that are consistent with those predicted from prior studies of CME density close to the Sun.