The hard X-ray spectrum of magnetic cataclysmic variables can be modelled to provide a measurement of white dwarf mass. This method is complementary to radial velocity measurements, which depend on the (typically rather uncertain) binary inclination. Here we present results from a Legacy Survey of 19 magnetic cataclysmic variables with NuSTAR.We fit accretion column models to their 20–78 keV spectra and derive the white dwarf masses, finding a weighted average M(sub WD) = 0.77 ± 0.02 M(sub ⨀), with a standard deviation σ = 0.10 M(sub ⨀), when we include the masses derived from previous NuSTAR observations of seven additional magnetic cataclysmic variables. We find that the mass distribution of accreting magnetic white dwarfs is consistent with that of white dwarfs in non-magnetic cataclysmic variables. Both peak at a higher mass than the distributions of isolated white dwarfs and post-common-envelope binaries. We speculate as to why this might be the case, proposing that consequential angular momentum losses may play a role in accreting magnetic white dwarfs and/or that our knowledge of how the white dwarf mass changes over accretion–nova cycles may also be incomplete.