Production of ${B}_{c}^{+}$ mesons in proton-proton collisions at a center-of-mass energy of 8 TeV is studied with data corresponding to an integrated luminosity of $2.0\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ recorded by the LHCb experiment. The ratio of production cross sections times branching fractions between the ${B}_{c}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}$ and ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}{K}^{+}$ decays is measured as a function of transverse momentum and rapidity in the regions $0<{p}_{T}<20\text{ }\text{ }\mathrm{GeV}/c$ and $2.0<y<4.5$. The ratio in this kinematic range is measured to be $(0.683\ifmmode\pm\else\textpm\fi{}0.018\ifmmode\pm\else\textpm\fi{}0.009)%$, where the first uncertainty is statistical and the second systematic.