A measurement of the ratio of semileptonic branching fractions $ℛ(J\psi )$, defined as $ℛ(J/\psi )\equiv ℬ(B_c^{+}\to J/\psi {\tau }^{+}{\nu }_{\tau })/ℬ(B_c^{+}\to J/\psi {\mu }^{+}{\nu }_{\mu })$, is reported using a sample of proton-proton collision data corresponding to an integrated luminosity of 5.4 fb${}^{-1}$ recorded by the LHCb experiment in 2016–2018 at a center-of-mass energy of 13 TeV. The measured value is found to be $ℛ(J/\psi )=0.51\pm 0.12\mathrm{\text{(stat)}}\pm 0.08\mathrm{\text{(syst)}}$, which is within 1.8 standard deviations of the predictions from the Standard Model assuming lepton flavor universality.