The production cross-section of a top quark in association with a W boson is measured using proton–proton collisions at $\sqrt{s} = 8\,\text {TeV}$. The dataset corresponds to an integrated luminosity of $20.2\,\text {fb}^{-1}$, and was collected in 2012 by the ATLAS detector at the Large Hadron Collider at CERN. The analysis is performed in the single-lepton channel. Events are selected by requiring one isolated lepton (electron or muon) and at least three jets. A neural network is trained to separate the tW signal from the dominant $t{\bar{t}}$ background. The cross-section is extracted from a binned profile maximum-likelihood fit to a two-dimensional discriminant built from the neural-network output and the invariant mass of the hadronically decaying W boson. The measured cross-section is $\sigma _{tW} = 26 \pm 7\,\text {pb}$, in good agreement with the Standard Model expectation.