  We bound the $Z^\prime tc$ coupling using the $D^{0}-\bar{D^{0}}$ meson
mixing system. We obtained such coupling which is less than $5.75\times
10^{-2}$. We have studied the $Z^\prime$ boson resonance considering single top
production in the $e^+e^-\to Z^\prime\to tc$ process. We obtained the number of
events which is expected to be less than $10^7$ at the International Linear
Collider scenario. We get a branching ratio of the order of $10^{-2}$ for the
$Z^\prime\to tc$ decay.
