  In the perturbative QCD (PQCD) approach we study the direct $CP$ violation in
$B^+_{c}\rightarrow D_{(s)}^+\rho^0(\omega) \rightarrow D_{(s)}^+\pi^+\pi^-$
via the $\rho-\omega$ mixing mechanism. We find that the $CP$ violation can be
enhanced by $\rho-\omega$ mixing when the invariant masses of the $\pi^+\pi^-$
pairs are in the vicinity of the $\omega$ resonance. For the decay process
$B^+_{c}\rightarrow D^+\rho^0(\omega) \rightarrow D^+\pi^+\pi^-$, the maximum
$CP$ violation can reach 7.5 {\%}.
