We present the first measurement of the production cross section of a W boson with a single charm quark (c) in pp collisions at s√=1.96  TeV, using soft muon tagging of c jets. In a data sample of ∼1.8  fb−1, recorded with the Collider Detector at Fermilab II detector at the Fermilab Tevatron, we select events with W+1 or 2 jets. We use the charge correlation between the W and the muon from the semileptonic decay of a charm hadron to extract the Wc signal. We measure σWc(pTc>20  GeV/c,|ηc|<1.5)×BR(W→ℓν)=9.8±3.2  pb, in agreement with theoretical expectations.