Multiple Coulomb scattering (MCS) is a well-known phenomenon occurring when charged particles traverse materials. Measurements of muons traversing low $Z$ materials made in the MuScat experiment showed that theoretical models and simulation codes, such as geant4 (v7.0), over-estimated the scattering. The Muon Ionization Cooling Experiment (MICE) measured the cooling of a muon beam traversing a liquid hydrogen or lithium hydride (LiH) energy absorber as part of a programme to develop muon accelerator facilities, such as a neutrino factory or a muon collider. The energy loss and MCS that occur in the absorber material are competing effects that alter the performance of the cooling channel. Therefore measurements of MCS are required in order to validate the simulations used to predict the cooling performance in future accelerator facilities. We report measurements made in the MICE apparatus of MCS using a LiH absorber and muons within the momentum range 160 to $245\mathrm{MeV}/c$. The measured RMS scattering width is about 9% smaller than that predicted by the approximate formula proposed by the Particle Data Group, but within the latter’s stated uncertainty. Data at 172, 200 and $240\mathrm{MeV}/c$ are compared to the geant4 (v9.6) default scattering model. These measurements show agreement with this more recent geant4 (v9.6) version over the range of incident muon momenta.