[en] We calculate the full one-loop electroweak radiative corrections to the cross section of single W-boson inclusive hadroproduction at finite transverse momentum (p_T). This includes the O(α) corrections to W+j production, the O(α_s) corrections to W+γ production, and the tree-level contribution from W+j photoproduction with one direct or resolved photon in the initial state. We present the integrated cross section as a function of a minimum-p_T cut as well as the p_T distribution for the experimental conditions at the Fermilab Tevatron and the CERN LHC and estimate the theoretical uncertainties. (orig.)