  Aspects of top quark physics can be studied at a future Circular
Electron-Positron Collider (CEPC). In particular, Flavor-Changing Neutral
Current interactions (FCNC) of the top quark can be studied even with a
center-of-mass energy from $\sqrt{s}\gtrsim m_t$ to $\sqrt{s}=240$ GeV, through
the production a single top quark in association with a charm quark, which can
arise in several scenarios of new physics. We explore here this signal within
the Left-Right Mirror Model, which is a Left-Right model that includes mirror
fermions; this model is motivated as a possible solution to the strong CP
problem and by its rich phenomenology. We find that for particular scenarios of
the model parameters, which are in agreement with the most up-to-date
experimental constraints, the signal coming from the process $e^+e^-\to V \to
tc$ ($V=Z,\,Z^{\prime}$) provide a detectable signal and thus it can give
evidence for FCNC interactions; in these scenarios the mass of a new neutral
gauge boson can be as high as $m_{Z'}=7$ TeV.
