We report on a search for the non-standard-model process u(c)+g→t using pp collision data collected by the Collider Detector at Fermilab II detector corresponding to 2.2  fb−1. The candidate events are classified as signal-like or backgroundlike by an artificial neural network. The observed discriminant distribution yields no evidence for flavor-changing neutral current top-quark production, resulting in an upper limit on the production cross section σ(u(c)+g→t)<1.8  pb at the 95% C.L. Using theoretical predictions we convert the cross section limit to upper limits on flavor-changing neutral current branching ratios: B(t→u+g)<3.9×10−4 and B(t→c+g)<5.7×10−3.