Ocean circulation and the marine carbon cycle can be indirectly inferred from stable and radiogenic carbon isotope ratios (σ13C, 14C, respectively), measured directly in the water column, or recorded in geological archives such as sedimentary microfossils and corals. However, interpreting these records is non-trivial because they reflect a complex interplay between physical and biogeochemical processes. By directly simulating multiple isotopic tracer fields within numerical models, we can improve our understanding of the processes that control large-scale isotope distributions and interpolate the spatiotemporal gaps in both modern and palaeo datasets. We have added the stable isotope 13C to the ocean component of the FAMOUS coupled atmosphere-ocean general circulation model, which is a valuable tool for simulating complex feedbacks between different Earth system processes on decadal to multi-millennial timescales. We tested three different biological fractionation parameterisations to account for the uncertainty associated with equilibrium fractionation during photosynthesis and used sensitivity experiments to quantify the effects of fractionation during air-sea gas exchange and primary productivity on the simulated σ13C CDIC distribution. Following a 10000-year pre-industrial spin-up, we simulated the Suess effect (the isotopic imprint of anthropogenic fossil fuel burning) to assess the performance of the model in replicating modern observations. Our implementation captures the large-scale structure and range of σ13C CDIC observations in the surface ocean, but the simulated values are too high at all depths, which we infer is due to biases in the biological pump. In the first instance, the new classCombining double low line"inline-formula">13C< tracer will therefore be useful for recalibrating both the physical and biogeochemical components of FAMOUS.