Measurements are presented of associated production of a W boson and a charm quark ( W+c ) in proton–proton collisions at a center-of-mass energy of 13 TeV . The data correspond to an integrated luminosity of 35.7 fb−1 collected by the CMS experiment at the CERN LHC. The W bosons are identified by their decay into a muon and a neutrino. The charm quarks are tagged via the full reconstruction of D∗(2010)± mesons that decay via D∗(2010)±→D0+π±→K∓+π±+π± . A cross section is measured in the fiducial region defined by the muon transverse momentum pμT>26GeV , muon pseudorapidity |ημ|<2.4 , and charm quark transverse momentum pcT>5GeV . The inclusive cross section for this kinematic range is σ(W+c)=1026±31(stat)+76−72(syst) pb . The cross section is also measured differentially as a function of the pseudorapidity of the muon from the W boson decay. These measurements are compared with theoretical predictions and are used to probe the strange quark content of the proton.