In this paper, we formulate radiatively induced QCD $\theta$ parameters through a loop-diagramatic approach. This method should be more robust derivation compared to an ordinary one: $\theta= \text{arg}\, \text{det} (M_u M_d)$, where $M_q$ is a loop-level quark mass matrix. For the application, we investigate the radiatively induced $\theta$ parameter in the minimal left-right symmetric model. We analytically confirmed an old result: two-loop induced $\theta$ parameter, corresponding to one-loop corrections to the quark mass matrices, completely vanishes. Furthermore, we estimate the size of a non-vanishing radiative $\theta$ parameter at three-loop level. We found that the induced neutron electric dipole moment can be smaller than the current experimental bounds.