  We present full-Stokes radio polarization observations of the quasar PKS
B2126-158 (z=3.268) from 1 to 10 GHz using the Australia Telescope Compact
Array. The source has large fractional circular polarization, m_c \equiv |V|/I,
detected at high significance across the entire band (from 15 to 90\sigma per
128 MHz sub-band). This allows us to construct the most robust circular
polarization (CP) spectrum of an AGN jet to date. We find m_c \propto
\nu^{+0.60\pm0.03} from 1.5 to 6.5 GHz, with a peak of m_c ~ 1% before the
spectrum turns over somewhere between 6.5 and 8 GHz, above which m_c \propto
\nu^{-3.0\pm0.4}. The fractional linear polarization (p) varies from <~0.2% to
~1% across our frequency range and is strongly anti-correlated with the
fractional CP, with a best-fit power law giving m_c \propto p^{-0.24\pm0.03}.
This is the first clear relation between the observed linear and circular
polarisations of an AGN jet, revealing the action of Faraday conversion of
linear polarization (LP) to CP within the jet. More detailed modelling in
conjunction with high-spatial resolution observations are required to determine
the true driving force behind the conversion (i.e. magnetic twist or internal
Faraday rotation). In particular determining whether the observed Faraday
rotation is internal or entirely external to the jet is key to this goal. The
simplest interpretation of our observations favours some internal Faraday
rotation, implying that Faraday rotation-driven conversion of LP to CP is the
dominant CP generation mechanism. In this case, a small amount of
vector-ordered magnetic field along the jet axis is required, along with
internal Faraday rotation from the low energy end of the relativistic electron
energy spectrum in an electron-proton dominated jet.
