A measurement of the ratio of the branching fractions of the $B^{+}\rightarrow K^{+}\mu^{+}\mu^{-}$ and $B^{+}\rightarrow K^{+}e^{+}e^{-}$ decays is presented using proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb$^{-1}$, recorded with the LHCb experiment at center-of-mass energies of 7 and 8 $\mathrm{\,Te\kern -0.1em V}$. The value of the ratio of branching fractions for the dilepton invariant mass squared range $1<q^{2}<6\mathrm{\,Ge\kern -0.1em V^2\!/}c^4$ is measured to be $0.745^{+0.090}_{-0.074}\mathrm{\,(stat)}\,\pm0.036\mathrm{\,(syst)}$. This value is the most precise measurement of the ratio of branching fractions to date and is compatible with the SM prediction within $2.6$ standard deviations.