The polarisation of prompt $psi(2S)$ mesons is measured by performing an angular analysis of $psi(2S)rightarrow mu^{+} mu^{-}$ decays using proton-proton collision data, corresponding to an integrated luminosity of 1.0 fb$^{-1}$, collected by the LHCb detector at a centre-of-mass energy of 7 TeV. The polarisation is measured in bins of transverse momentum $p_mathrm{T}$ and rapidity $y$ in the kinematic region $3.5<p_mathrm{T}<15$ GeV$/c$ and $2.0<y<4.5$, and is compared to theoretical models. No significant polarisation is observed.