A new method of momentum measurement of charged particles through multiple Coulomb scattering (MCS) in the OPERA lead-emulsion target is presented. It is based on precise measurements of track angular deviations carried out thanks to the very high resolution of nuclear emulsions. The algorithm has been tested with Monte Carlo pions. The results are found to describe within the expected uncertainties the data obtained from test beams. We also present a comparison of muon momenta evaluated through MCS in the OPERA lead-emulsion target with those determined by the electronic detectors for neutrino-charged current interaction events. The two independent measurements agree within the experimental uncertainties, and the results validate the algorithm developed for the emulsion detector of OPERA.