Abstract Polarimetric observations of fast radio bursts (FRBs) are a powerful resource for better understanding these mysterious sources by directly probing the emission mechanism of the source and the magneto-ionic properties of its environment. We present a pipeline for analyzing the polarized signal of FRBs captured by the triggered baseband recording system operating on the FRB survey of The Canadian Hydrogen Intensity Mapping Experiment (CHIME/FRB). Using a combination of simulated and real FRB events, we summarize the main features of the pipeline and highlight the dominant systematics affecting the polarized signal. We compare parametric (QU-fitting) and non-parametric (rotation measure synthesis) methods for determining the Faraday rotation measure (RM) and find the latter method susceptible to systematic errors from known instrumental effects of CHIME/FRB observations. These errors include a leakage artifact that appears as polarized signal near RM ∼ 0 rad m⁻² and an RM sign ambiguity introduced by path length differences in the system’s electronics. We apply the pipeline to a bright burst previously reported (FRB 20191219F), detecting an RM of +6.074 ± 0.006 ± 0.050 rad m⁻² with a significant linear polarized fraction (≳0.87) and strong evidence for a non-negligible circularly polarized component. Finally, we introduce an RM search method that employs a phase-coherent de-rotation algorithm to correct for intra-channel depolarization in data that retain electric field phase information and successfully apply it to an unpublished FRB, FRB 20200917A, measuring an RM of −1294.47 ± 0.10 ± 0.05 rad m⁻² (the second largest unambiguous RM detection from any FRB source observed to date).