We present a measurement of the direct $CP$-violating charge asymmetry in ${B}^{\ifmmode\pm\else\textpm\fi{}}$ mesons decaying to $J/\ensuremath{\psi}{K}^{\ifmmode\pm\else\textpm\fi{}}$ and $J/\ensuremath{\psi}{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ where $J/\ensuremath{\psi}$ decays to ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$, using the full run II data set of $10.4\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of proton-antiproton collisions collected using the D0 detector at the Fermilab Tevatron Collider. A difference in the yield of ${B}^{\ensuremath{-}}$ and ${B}^{+}$ mesons in these decays is found by fitting to the difference between their reconstructed invariant mass distributions resulting in asymmetries of ${A}^{J/\ensuremath{\psi}K}=[0.59\ifmmode\pm\else\textpm\fi{}0.37]%$, which is the most precise measurement to date, and ${A}^{J/\ensuremath{\psi}\ensuremath{\pi}}=[\ensuremath{-}4.2\ifmmode\pm\else\textpm\fi{}4.5]%$. Both measurements are consistent with standard model predictions.