  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(alpha) corrections to W+j production, the
O(alpha_s) corrections to W+gamma 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.
