The top quark pair production cross section ($\sigma_{\mathrm{t}\overline{\mathrm{t}}}$) is measured for the first time in pp collisions at a center-of-mass energy of 5.02 TeV. The data were collected by the CMS experiment at the LHC and correspond to an integrated luminosity of 27.4 pb$^{-1}$. The measurement is performed by analyzing events with at least one charged lepton. The measured cross section is $ \sigma_{\mathrm{t}\overline{\mathrm{t}}} = 69.5 \pm 6.1$ (stat) $\pm 5.6$ (syst) $\pm 1.6$ (lumi) pb, with a total relative uncertainty of 12%. The result is in agreement with the expectation from the standard model. The impact of the presented measurement on the determination of the gluon distribution function is investigated.