Numerous reconstructions of global climate and the carbon cycle have underpinned conceptual models of the governing feedbacks driving their interaction. However, causal relationships between such reconstructions and their quantification are required to understand the driving mechanisms of past global climate change. Here, utilizing continuous high-resolution deep ocean foraminifer stable carbon and oxygen isotope ratios for the past 66 million years, we inspect the causal relations in the climate-carbon cycle system using machine learning approaches. We find that these records are strongly causally related in some periods, particularly during warm climate states, but causation is insignificant in other periods. Intriguingly, the causal dynamics appear to be influenced by long-term modulation cycles of eccentricity and obliquity, suggesting an orbital influence on the mechanistic coupling between climate and carbon cycling. Moreover, our results are consistent with strengthening positive feedbacks between the global carbon cycle and the climate leading towards both abrupt warming and cooling events hypothesized to be due to the passing of tipping points.