The inclusive cross section for the production of a single top quark in association with a W boson is measured using 140 fb^-1 of proton-proton collision data collected with the ATLAS detector at √s = 13 TeV. Events containing two charged leptons and at least one jet identified as originating from a b-quark are selected. A multivariate discriminant is constructed to separate the tW signal from the tt<over bar> background. The cross section is extracted using a profile likelihood fit to the signal and control regions and it is measured to be σ_tW = 75_-14⁺¹⁵ pb, in good agreement with the Standard Model prediction. The measured cross section is used to extract a value for the left-handed form factor at the Wtb vertex times the CabibboKobayashi-Maskawa matrix element ∣f_LVV_tb∣ of 0.97 ± 0.10.