  We report on the first search for top-quark production via flavor-changing
neutral-current (FCNC) interactions in the non-standard-model process u(c)+g ->
t using ppbar collision data collected by the CDF II detector. The data set
corresponds to an integrated luminosity of 2.2/fb. The candidate events feature
the signature of semileptonic top-quark decays and are classified as
signal-like or background-like by an artificial neural network trained on
simulated events. The observed discriminant distribution is in good agreement
with the one predicted by the standard model and provides no evidence for FCNC
top-quark production, resulting in a Bayesian upper limit on the production
cross section sigma (u(c)+g -> t) < 1.8 pb at the 95% confidence level. Using
theoretical predictions we convert the cross-section limit to upper limits on
FCNC branching ratios: BR (t -> u+g) < 3.9 x 10{-4}$ and BR (t -> c+g) < 5.7 x
10^{-3}.
