(1) Background: Radioprotective agents have garnered considerable interest due to their prospective applications in radiotherapy, public health medicine, and situations of large-scale accidental radiation exposure or impending radiological emergencies. Cystamine, an organic diamino–disulfide compound, is recognized for its radiation-protective and antioxidant properties. This study aims to utilize the aqueous ferrous sulfate (Fricke) dosimeter to measure the free-radical scavenging capabilities of cystamine during irradiation by fast carbon ions. This analysis spans an energy range from 6 to 500 MeV per nucleon, which correlates with “linear energy transfer” (LET) values ranging from approximately 248 keV/μm down to 9.3 keV/μm. (2) Methods: Monte Carlo track chemistry calculations were used to simulate the radiation-induced chemistry of aerated Fricke–cystamine solutions across a broad spectrum of cystamine concentrations, ranging from 10−6 to 1 M. (3) Results: In irradiated Fricke solutions containing cystamine, cystamine is observed to hinder the oxidation of Fe2+ ions, an effect triggered by oxidizing agents from the radiolysis of acidic water, resulting in reduced Fe3+ ion production. Our simulations, conducted both with and without accounting for the multiple ionization of water, confirm cystamine’s ability to capture free radicals, highlighting its strong antioxidant properties. Aligning with prior research, our simulations also indicate that the protective and antioxidant efficiency of cystamine diminishes with increasing LET of the radiation. This result can be attributed to the changes in the geometry of the track structures when transitioning from lower to higher LETs. (4) Conclusions: If we can apply these fundamental research findings to biological systems at a physiological pH, the use of cystamine alongside carbon-ion hadrontherapy could present a promising approach to further improve the therapeutic ratio in cancer treatments.