  We present a calculation of the next-to-leading-order electroweak corrections
to W+\gamma\ production, including the leptonic decay of the W boson and taking
into account all off-shell effects of the W boson, where the finite width of
the W boson is implemented using the complex-mass scheme. Corrections induced
by incoming photons are fully included and find particular emphasis in the
discussion of phenomenological predictions for the LHC. The corresponding
next-to-leading-order QCD corrections are reproduced as well. In order to
separate hard photons from jets, a quark-to-photon fragmentation function a la
Glover and Morgan is employed. Our results are implemented into Monte Carlo
programs allowing for the evaluation of arbitrary differential cross sections.
We present integrated cross sections for the LHC at 7TeV, 8TeV, and 14TeV as
well as differential distributions at 14TeV for bare muons and dressed leptons.
Finally, we discuss the impact of anomalous WW\gamma\ couplings.
