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Radio emission during X-ray binary outbursts is dominated by synchrotron radiation from relativistic jets, but is usually studied through total-intensity diagnostics such as flux density, spectra, variability, and proper motion. Radio spectropolarimetry provides a complementary probe of the magneto-ionic plasma through Faraday rotation and depolarisation. When the Faraday rotating material is local to the source, these effects can constrain the jet plasma composition and mass content, but this approach is rarely applied to transient jetted sources. We present MeerKAT L-band spectropolarimetry of the black hole X-ray binary Swift J1727 during its 2023 outburst, focusing on the brightest radio flaring interval, when relativistic jets were being launched intermittently. Using multiple spectropolarimetric techniques, we identify transient Faraday-complex structure coincident with the major radio flares. The close temporal association with the flaring activity, together with the stability of the foreground Faraday screen, favours an origin local to the jet rather than in the ISM or in a separate local screen external to the emitting plasma. Since internal Faraday rotation is suppressed in a pure electron-positron plasma, the data favour a dominant electron-proton component. Interpreting the characteristic Faraday thickness as internal rotation, and anchoring the magnetic-field and size scales with synchrotron self-absorption arguments, we infer a characteristic Faraday-rotating mass of order M<SUB>rot</SUB> ~ 10<SUP>21</SUP> g, corresponding to only a small fraction, f<SUB>rot</SUB> ~ 10<SUP>-3</SUP>, of the accreted mass available during the flare. These results show that time-domain spectropolarimetry can turn transient Faraday complexity into a diagnostic of jet composition, mass loading, and plasma evolution in X-ray binary outbursts, and potentially other transient jetted sources.