The active young protostar DG Tau has an extended jet that has been well studied at radio, optical, and X-ray wavelengths. We report sensitive new VLA full-polarization observations of the core and jet between 5 GHz and 8 GHz. Our high angular resolution observation at 8 GHz clearly shows an unpolarized inner jet with a size 42 AU (0.35) extending along a position angle similar to the optical-X ray outer jet. Using our nearly coeval 2012 VLA observations, we find a spectral-index=+0.46+/-0.05, which combined with the lack of polarization, is consistent with bremsstrahlung (free-free) emission, with no evidence for a non-thermal coronal component. By identifying the end of the radio jet as the optical depth unity surface, and calculating the resulting emission measure, we find our radio results are in agreement with previous optical line studies of electron density and consequent mass-loss rate. We also detect a weak radio knot at 5 GHz located 7 from the base of the jet, coincident with the inner radio knot detected by Rodriguez et al. (2012) in 2009 but at lower surface brightness. We interpret this as due to expansion of post-shock ionized gas in the three years between observations.