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