The production of $\varXi _{cc}^ {++}$ baryons in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13\;{\rm{TeV}}$ is measured in the transverse-momentum range $4 \lt p_{\rm{T}} \lt 15\;{\rm{GeV}}/c$ and the rapidity range $2.0 \lt y \lt 4.5$. The data used in this measurement correspond to an integrated luminosity of $1.7\;{\rm{fb}}^{-1}$, recorded by the LHCb experiment during 2016. The ratio of the $\varXi _{cc}^ {++}$ production cross-section times the branching fraction of the $\varXi _{cc}^ {++} \to \varLambda _c^ + K^-\pi^+ \pi^+$ decay relative to the prompt $\varLambda _c^ + $ production cross-section is found to be $(2.22\pm 0.27 \pm 0.29)\times 10^{-4}$, assuming the central value of the measured $\varXi _{cc}^ {++}$ lifetime, where the first uncertainty is statistical and the second systematic.