We report on a search for the non-standard-model process u(c)+g→t using pp̅ collision data collected by the Collider Detector at Fermilab II detector corresponding to 2.2 fb[superscript -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[superscript -4] and B(t→c+g)<5.7×10[superscript -3]. Academy of Finland Slovak R&D Agency Programa Consolider-Ingenio 2010, Spain Ministerio de Ciencia e Innovación, Spain Russian Foundation for Basic Research Institut National de Physique Nucleaire et Physique des Particules/CNRS Royal Society, United Kingdom Science and Technology Facilities Council, United Kingdom Korean Research Foundation Korean Science and Engineering Foundation Bundesministerium für Bildung und Forschung, Germany Alfred P. Sloan Foundation Swiss National Science Foundation National Science Council of the Republic of China Natural Sciences and Engineering Research Council of Canada Ministry of Education, Culture, Sports, Science and Technology of Japan Italian Istituto Nazionale di Fisica Nucleare National Science Foundation United States Department of Energy