  We discuss the associated production of a top quark with a photon via
anomalous $t$-$q$-$\gamma$ couplings, and present higher-order corrections from
soft-gluon emission for the processes $gq \rightarrow t\gamma$ at LHC energies.
We perform soft-gluon resummation at next-to-leading-logarithm accuracy and
derive approximate next-to-next-to-leading order (aNNLO) double-differential
cross sections. We calculate at aNNLO the total $t\gamma$ production cross
sections and the top-quark transverse-momentum and rapidity distributions for
various LHC energies, and show that the soft-gluon corrections are large and
dominant in these processes.
