The strange quark content of the proton is probed through the measurement of the production cross section for a W boson and a charm (c) quark in proton-proton collisions at a center-of-mass energy of 13 TeV. The analysis uses a data sample corresponding to a total integrated luminosity of 138 fb(-1) collected with the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm jets are tagged using the presence of a muon or a secondary vertex inside the jet. The W + c production cross section and the cross section ratio R-c(+/-) = sigma(W+ + (c) over bar)/sigma(W- + c) are measured inclusively and differentially as functions of the transverse momentum and the pseudorapidity of the lepton originating from the W boson decay. The precision of the measurements is improved with respect to previous studies, reaching 1% in R-c(+/-) = 0.950 +/- 0.005 (stat)+/- 0.010 (syst). The measurements are compared with theoretical predictions up to next-to-next-to-leading order in perturbative quantum chromodynamics.