A measurement of the production of a prompt J/ψ meson in association with a W$^{±}$ boson with W$^{±}$ → μν and J/ψ → μ$^{+}$μ$^{−}$ is presented for J/ψ transverse momenta in the range 8.5–150 GeV and rapidity |y$_{J/ψ}$| < 2.1 using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton-proton centre-of-mass energy of $ \sqrt{s} $ = 8 TeV and correspond to an integrated luminosity of 20.3 fb$^{−1}$. The ratio of the prompt J/ψ plus W$^{±}$ cross-section to the inclusive W$^{±}$ cross-section is presented as a differential measurement as a function of J/ψ transverse momenta and compared with theoretical predictions using different double-parton-scattering cross-sections.