We present the results of an Australia Telescope Compact Array 1.4GHz spectropolarimetric aperture synthesis survey of 34deg^2^ centered on Centaurus A-NGC 5128. A catalog of 1005 extragalactic compact radio sources in the field to a continuum flux density of 3mJy/beam is provided along with a table of Faraday rotation measures (RMs) and linear polarized intensities for the 28% of sources with high signal to noise in linear polarization. We use the ensemble of 281 background polarized sources as line-of-sight probes of the structure of the giant radio lobes of Centaurus A. This is the first time such a method has been applied to radio galaxy lobes and we explain how it differs from the conventional methods that are often complicated by depth and beam depolarization effects. Assuming a magnetic field strength in the lobes of 1.3B1uG, where B1=1 is implied by equipartition between magnetic fields and relativistic particles, the upper limit we derive on the maximum possible difference between the average RM of 121 sources behind Centaurus A and the average RM of the 160 sources along sightlines outside Centaurus A implies an upper limit on the volume-averaged thermal plasma density in the giant radio lobes of <ne><5x10^-5^B1^-1^cm^-3^. We use an RM structure function analysis and report the detection of a turbulent RM signal, with rms=17rad/m^2^ and scale size 0.3deg, associated with the southern giant lobe. We cannot verify whether this signal arises from turbulent structure throughout the lobe or only in a thin skin (or sheath) around the edge, although we favor the latter. The RM signal is modeled as possibly arising from a thin skin with a thermal plasma density equivalent to the Centaurus intragroup medium density and a coherent magnetic field that reverses its sign on a spatial scale of 20kpc. For a thermal density of n1 10^-3^cm^-3^, the skin magnetic field strength is 0.8n1^-1^uG.