Primordial abundances of light elements are sensitive to the physics of the early Universe and can directly constrain cosmological quantities, such as the baryon-to-photon ratio $\eta _{10}$, the baryon density, and the number of neutrino families. Deuterium is especially suited for these studies: its primordial abundance is sensitive and monotonically dependent on $\eta _{10}$, allowing an independent measurement of the cosmic baryon density that can be compared, for instance, against the Planck satellite data. The primordial deuterium abundance can be measured in high H I column density absorption systems towards distant quasars. We report here a new measurement, based on high-resolution ESPRESSO data, of the primordial D I abundance of a system at redshift $z \sim 3.572$, towards PKS1937-101. Using only ESPRESSO data, we find a D /H ratio of $2.638\pm 10^{-5}$, while including the available UVES data improves the precision, leading to a ratio of $2.608 \pm 10^{-5}$. The results of this analysis agree with those of the most precise existing measurements. We find that the relatively low column density of this system ($\log {N_{\rm H_I}/ {\rm cm}^{-2}}\sim 18$) introduces modelling uncertainties, which become the main contributor to the error budget.