A theoretical study of photoexcitation of highly charged ions from their ground states, a process which can be realized at the Gamma Factory at CERN, is presented. Special attention is paid to the question of how the excitation rates are affected by the mixing of opposite‐parity ionic levels, which is induced both by an external electric field and the weak interaction between electrons and the nucleus. In order to reinvestigate this “Stark‐plus‐weak‐interaction” mixing, well‐known in neutral atomic systems, we employ relativistic Dirac theory. Based on the developed approach, detailed calculations are performed for the 1s1/2→$_{1/2} \rightarrow$ 2s1/2 and 1normals20.28em2normals1/2→1normals20.28em3normals1/2${\rm 1s}^2 \; {\rm 2s}_{1/2} \rightarrow {\rm 1s}^2 \; {\rm 3s}_{1/2}$ (M1 + parity–violating–E1) transitions in hydrogen‐ and lithium‐like ions, respectively. In particular, we focus on the difference between the excitation rates obtained for the right‐ and left‐circularly polarized incident light. This difference arises due to the parity violating mixing of ionic levels and is usually characterized in terms of the circular–dichroism parameter. We argue that future measurements of circular dichroism, performed with highly charged ions in the SPS or LHC rings, may provide valuable information on the electron–nucleus weak–interaction coupling.