Plasma screening effects on inelastic Compton scattering of photons by bound atomic electrons of hydrogenic target ions in weakly coupled plasmas are investigated. The particle interaction potential in weakly coupled plasmas is obtained using the Debye–Hückel model. The screened wave functions and energy eigenvalues for the ground and excited states of the target ion are obtained using the Ritz variational method. The expression for the lowest-order transition matrix element is obtained from a two-photon process associated with terms quadratic in the vector potential A. The inelastic Compton scattering cross-section from the 1s ground state to the 2p excited state is obtained as a function of the incident photon energy, including plasma screening effects. It is found that plasma screening effects significantly reduce the inelastic Compton scattering cross-section.