The integral cross section of the C-12(n,p)B-12 reaction has been determined for the first time in the neutron energy range from threshold to several GeV at the n_TOF facility at CERN. The measurement relies on the activation technique with the beta decay of B-12 measured over a period of four half-lives within the same neutron bunch in which the reaction occurs. The results indicate that model predictions, used in a variety of applications, are mostly inadequate. The value of the integral cross section reported here can be used as a benchmark for verifying or tuning model calculations.