  The precise determination of the $B_c \to \tau\nu_\tau$ branching ratio
provides an advantageous opportunity for understanding the electroweak
structure of the Standard Model, measuring the CKM matrix element $|V_{cb}|$
and probing new physics models. In this paper, we discuss the potential of
measuring the processes of $B_c \to \tau\nu_\tau$ with $\tau$ decaying
leptonically at the proposed Circular Electron Positron Collider (CEPC). We
conclude that during the $Z$ pole operation, the channel signal can achieve
five $\sigma$ significance with $\sim 10^9$ $Z$ decays, and the signal strength
accuracies for $B_c \to \tau\nu_\tau$ can reach around 1% level at the nominal
CEPC $Z$ pole statistics of one trillion $Z$ decays assuming the total $B_c \to
\tau \nu_\tau$ yield is $3.6 \times 10^6$. Our theoretical analysis indicates
the accuracy could provide a strong constraint on the general effective
Hamiltonian for the $b \to c\tau\nu$ transition. If the total $B_c$ yield can
be determined to $\mathcal{O}(1\%)$ level of accuracy in the future, these
results also imply $|V_{cb}|$ could be measured up to $\mathcal{O}(1\%)$ level
of accuracy.
