We use the Yang-Mills gradient flow to study the mixing of $CP$-violating pure gauge operators in continuum QCD with special attention to Weinberg’s $d=6$ purely gluonic operator. The gradient flow allows for a relatively clear derivation of the Wilson coefficients of the $CP$-violating effective Hamiltonian. This calculation is the first step towards a high-energy matching of matrix elements involving the $CP$-violating operators between the perturbative and lattice regimes.