We report on a search for the non-standard-model process u(c) + g --> t using pp[over ] 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 sigma(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 x 10;{-4} and B(t --> c + g) < 5.7 x 10;{-3}.