  We present a next-to-leading order QCD calculation of the cross section for
isolated large-p_T prompt photon production in collisions of transversely
polarized protons. We devise a simple method of dealing with the phase space
integrals in dimensional regularization in the presence of the cos(2 phi)
azimuthal-angular dependence occurring for transverse polarization. Our results
allow to calculate the double-spin asymmetry A_TT for this process at
next-to-leading order accuracy, which may be used at BNL-RHIC to measure the
transversity parton distributions of the proton.
