  In the present work the $Z^\prime tc$ coupling is bounded by using the
current experimental data on the $D^{0}-\bar{D^{0}}$ meson-mixing system. It is
found that the strength associated to this coupling is less than $5.75\times
10^{-2}$. The single top production through the $e^+e^-\to Z^\prime\to tc$
process at the $Z^\prime$ boson resonance is studied and we found that around
$10^7$ $tc$ events will be expected at the International Linear Collider. For
the $Z^\prime\to tc$ decay, we predict a branching ratio of $10^{-2}$.
