The endothermic nuclear reaction between thermal tritons and high-energy protons can represent an important contribution to the total neutron yield in tokamak plasmas heated by radio-frequency waves, as the first JET experiments have demonstrated (see Mantsinen et al 2001 Nucl. Fusion 41 1815). A further study based on more recent JET experiments was reported in Santala et al 2006 (Plasma Phys. Control. Fusion 48 1233). In this letter we supplement and complete the previous analysis by reporting the first systematic measurement of the scaling of the proton-triton (pT) thermo-nuclear fusion reaction rate as a function of the total energy content and perpendicular tail temperature of the fast protons heated by radio-frequency waves. It is found that the pT-neutron rate increases almost linearly with the fast proton temperature and the total energy content.