  We study the next-to-leading order perturbative QCD corrections to the
transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron
production in lepton-proton deep inelastic scattering. The corresponding
differential cross section is evaluated as a convolution of a twist-three
quark-gluon correlation function, often referred to as Qiu-Sterman function,
the usual unpolarized fragmentation function, and a hard coefficient function.
By studying the collinear divergence structure, we identify the evolution
kernel for the Qiu-Sterman function. The hard coefficient function, which is
finite and free of any divergence, is evaluated at one-loop order.
