The precise measurement of the spectrum of protons, the most abundant component of the cosmic radiation, is necessary to understand the source and acceleration of cosmic rays in the Milky Way. This work reports the measurement of the cosmic ray proton fluxes with kinetic energies from 40 GeV to 100 TeV, with 2 1/2 years of data recorded by the DArk Matter Particle Explorer (DAMPE). This is the first time that an experiment directly measures the cosmic ray protons up to ~100 TeV with high statistics. The measured spectrum confirms the spectral hardening at ~300 GeV found by previous experiments and reveals a softening at ~13.6 TeV, with the spectral index changing from ~2.60 to ~2.85. Our result suggests the existence of a new spectral feature of cosmic rays at energies lower than the so-called knee and sheds new light on the origin of Galactic cosmic rays.