Abstract. Cenozoic stable carbon (δ13C) and oxygen (δ18O) isotope ratios of deep-sea foraminiferal calcite co-vary with the 405 kyr eccentricity cycle, suggesting a link between orbital forcing, the climate system, and the carbon cycle. Variations in δ18O are partly forced by ice-volume changes that have mostly occurred since the Oligocene. The cyclic δ13C–δ18O co-variation is found in both ice-free and glaciated climate states, however. Consequently, there should be a mechanism that forces the δ13C cycles independently of ice dynamics. In search of this mechanism, we simulate the response of several key components of the carbon cycle to orbital forcing in the Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir model (LOSCAR). We force the model by changing the burial of organic carbon in the ocean with various astronomical solutions and noise and study the response of the main carbon cycle tracers. Consistent with previous work, the simulations reveal that low-frequency oscillations in the forcing are preferentially amplified relative to higher frequencies. However, while oceanic δ13C mainly varies with a 405 kyr period in the model, the dynamics of dissolved inorganic carbon in the oceans and of atmospheric CO2 are dominated by the 2.4 Myr cycle of eccentricity. This implies that the total ocean and atmosphere carbon inventory is strongly influenced by carbon cycle variability that exceeds the timescale of the 405 kyr period (such as silicate weathering). To test the applicability of the model results, we assemble a long (∼22 Myr) δ13C and δ18O composite record spanning the Eocene to Miocene (34–12 Ma) and perform spectral analysis to assess the presence of the 2.4 Myr cycle. We find that, while the 2.4 Myr cycle appears to be overshadowed by long-term changes in the composite record, it is present as an amplitude modulator of the 405 and 100 kyr eccentricity cycles.