We measure the cross section and the difference in rapidities between photons and charged leptons for inclusive $W(\ensuremath{\rightarrow}l\ensuremath{\nu})+\ensuremath{\gamma}$ production in $e\ensuremath{\gamma}$ and $\ensuremath{\mu}\ensuremath{\gamma}$ final states. Using data corresponding to an integrated luminosity of $4.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the D0 detector at the Fermilab Tevatron Collider, the measured cross section times branching fraction for the process $p\overline{p}\ensuremath{\rightarrow}W\ensuremath{\gamma}+X\ensuremath{\rightarrow}l\ensuremath{\nu}\ensuremath{\gamma}+X$ and the distribution of the charge-signed photon-lepton rapidity difference are found to be in agreement with the standard model. These results provide the most stringent limits on anomalous $WW\ensuremath{\gamma}$ couplings for data from hadron colliders: $\ensuremath{-}0.4<\ensuremath{\Delta}{\ensuremath{\kappa}}_{\ensuremath{\gamma}}<0.4$ and $\ensuremath{-}0.08<{\ensuremath{\lambda}}_{\ensuremath{\gamma}}<0.07$ at the 95% C.L.