The FASER detector at the LHC is designed to search for light and weakly-interacting particles, and to perform neutrino physics measurements. The emulsion detector is a crucial component of FASER, providing high-precision tracking of charged particles. In this paper, we describe the method for measuring the momentum of charged particles using the effect of multiple Coulomb scattering (MCS) on particle trajectories within the emulsion detector. The method involves reconstructing particle trajectories from aligned silver grains in emulsion films. We use MC simulations (Geant4) to evaluate the performance of this approach. The detector’s spatial resolution is typically 0.2 to 0.3 um in the transverse plane, enabling momentum determination from a few GeV up to a few TeV.