Magnetic fields play vital roles in intracluster media (ICMs), but estimating their strengths and distributions from observations is a major challenge. Faraday rotation measures (RMs) are widely applied to this task, so it is critical to understand inherent uncertainties in RM analysis. In this paper, we seek to characterize those uncertainties given the types of information available today, independent of the specific technique used. We conduct synthetic RM observations through the ICM of a galaxy cluster drawn from a magnetohydrodynamic cosmological simulation in which the magnetic field is known. We analyze the synthetic RM observations using an analytical formalism based on commonly used model assumptions, allowing us to relate model physical variables to outcome uncertainties. Despite the simplicity of some assumptions, and unknown physical parameters, we are able to extract an approximate magnitude of the central magnetic field within an apparently irreducible uncertain factor of ≈3. Principal, largely irreducible, uncertainties come from the unknown depth along the line of sight of embedded polarized sources, the lack of robust coherence lengths from area-constrained polarization sampling, and the unknown scaling between ICM electron density and magnetic field strength. The RM-estimated central magnetic field strengths span more than an order of magnitude including the full range of synthetic experiments.