  Renormalization factors for $\Delta S =1$ four-quark operators in the
effective weak Hamiltonian are perturbatively evaluated in domain-wall QCD. The
one-loop corrections of $\Delta S=1$ four-quark operators consist of two types
of diagrams: one is gluon exchange between quark lines and the other is penguin
diagrams containing quark loops. Combining both contributions, our results
allow a lattice calculation of the amplitude for $K\to \pi\pi$ decays with
$O(g^2)$ corrections included.
