We search for the production of single top quarks via flavor-changing neutral current couplings of a gluon to the top quark and a charm ($c$) or up ($u$) quark. We analyze 230 pb$^{-1}$ of lepton + jets data from $\ppbar$ collisions at a center of mass energy of 1.96 TeV collected by the D0 detector at the Fermilab Tevatron Collider. We observe no significant deviation from standard model predictions, and hence set upper limits on the anomalous coupling parameters $\kappacLambda$ and $\kappauLambda$, where $\kappag$ define the strength of $tcg$ and $tug$ couplings, and $\Lambda$ defines the scale of new physics. The limits at 95% C.L. are: $\kappacLambda < 0.15 \rm TeV^{-1}$ and $\kappauLambda < 0.037 \rm TeV^{-1}$.