Abstract The production cross-section of a top quark in association with a W boson is measured using proton–proton collisions at $$\sqrt{s} = 8\,\text {TeV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>8</mml:mn><mml:mspace/><mml:mtext>TeV</mml:mtext></mml:mrow></mml:math> . The dataset corresponds to an integrated luminosity of $$20.2\,\text {fb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>20.2</mml:mn><mml:mspace/><mml:msup><mml:mtext>fb</mml:mtext><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> , 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 $$t{\bar{t}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi><mml:mover><mml:mrow><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> 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 $$\sigma _{tW} = 26 \pm 7\,\text {pb}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>tW</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>26</mml:mn><mml:mo>±</mml:mo><mml:mn>7</mml:mn><mml:mspace/><mml:mtext>pb</mml:mtext></mml:mrow></mml:math> , in good agreement with the Standard Model expectation.