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Polarimetric observations of Fast Radio Bursts (FRBs) are a powerful resourcefor better understanding these mysterious sources by directly probing theemission mechanism of the source and the magneto-ionic properties of itsenvironment. We present a pipeline for analysing the polarized signal of FRBscaptured by the triggered baseband recording system operating on the FRB surveyof The Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB). Using acombination of simulated and real FRB events, we summarize the main features ofthe pipeline and highlight the dominant systematics affecting the polarizedsignal. We compare parametric (QU-fitting) and non-parametric (rotation measuresynthesis) methods for determining the Faraday rotation measure (RM) and findthe latter method susceptible to systematic errors from known instrumentaleffects of CHIME/FRB observations. These errors include a leakage artefact thatappears as polarized signal near $\rm{RM\sim 0 \; rad \, m^{-2}}$ and an RMsign ambiguity introduced by path length differences in the system'selectronics. We apply the pipeline to a bright burst previously reported by\citet[FRB 20191219F;][]{Leung2021}, detecting an $\mathrm{RM}$ of $\rm{+6.074\pm 0.006 \pm 0.050 \; rad \, m^{-2}}$ with a significant linear polarizedfraction ($\gtrsim0.87$) and strong evidence for a non-negligible circularlypolarized component. Finally, we introduce an RM search method that employs aphase-coherent de-rotation algorithm to correct for intra-channeldepolarization in data that retain electric field phase information, andsuccessfully apply it to an unpublished FRB, FRB 20200917A, measuring an$\mathrm{RM}$ of $\rm{-1294.47 \pm 0.10 \pm 0.05 \; rad \, m^{-2}}$ (the secondlargest unambiguous RM detection from any FRB source observed to date).

A Polarization Pipeline for Fast Radio Bursts Detected by CHIME/FRB