  In this paper, we calculate the branching ratio and direct CP asymmetry
parameter of $B_c^{\pm}\to D^{0}K^{\pm}$ in the framework of perturbative QCD
approach based on $k_T$ factorization. Besides the usual factorizable diagrams,
both non-factorizable and annihilation type contributions are taken into
account. We find that (a) the branching ratio is at the order of $10^{-5}$; (b)
the tree annihilation diagrams and the penguin diagrams dominate the total
contribution; and (c) the direct CP asymmetry is about 7%, which can be tested
in the Large Hadron Collider beauty experiments (LHC-b) at CERN.
