Measurements are presented of associated production of a $\mathrm {W}$ boson and a charm quark ( $\mathrm {W}+\mathrm {c}$ ) in proton–proton collisions at a center-of-mass energy of 13 $,\text {Te}\text {V}$ . The data correspond to an integrated luminosity of 35.7 $,\text {fb}^{-1}$ collected by the CMS experiment at the CERN LHC. The $\mathrm {W}$ bosons are identified by their decay into a muon and a neutrino. The charm quarks are tagged via the full reconstruction of ${\mathrm {D}^{}(2010)^{\pm }}$ mesons that decay via ${\mathrm {D}^{}(2010)^{\pm }}\rightarrow \mathrm {D}^0 + {\pi ^{\pm }}\rightarrow \mathrm {K}^{\mp } + {\pi ^{\pm }}+ {\pi ^{\pm }}$ . A cross section is measured in the fiducial region defined by the muon transverse momentum $p_{\mathrm {T}} ^{\mu } > 26,\text {Ge}\text {V} $ , muon pseudorapidity $|\eta ^{\mu } | < 2.4$ , and charm quark transverse momentum $p_{\mathrm {T}} ^{\mathrm {c}} > 5,\text {Ge}\text {V} $ . The inclusive cross section for this kinematic range is $\sigma (\mathrm {W}+\mathrm {c})=1026\pm 31,\text {(stat)} \begin{array}{c} +76\ -72 \end{array},\text {(syst)} \text { pb} $ . The cross section is also measured differentially as a function of the pseudorapidity of the muon from the $\mathrm {W}$ boson decay. These measurements are compared with theoretical predictions and are used to probe the strange quark content of the proton.