The enzyme rubisco catalyzes the first step of carbon assimilation in photosynthesis. Despite the massive flux of CO2 passing through this active site over billions of years, extant rubisco has relatively slow kinetics and is prone to off-target activity. In many growth regimes, this limits photosynthesis in planta. Many attempts have been made to improve the kinetic parameters of rubisco with limited success, potentially due to biochemical trade-offs. To understand the structural basis of constraints on rubisco, a comprehensive map of rubisco at the individual amino-acid level is needed. To that end we performed a deep mutational scan using a rubisco-dependent E. coli strain. By titrating CO2 concentrations it was possible to determine estimations for both catalytic rate (kcat) and substrate affinity (KM) of >99% of rubisco point mutants. Some positions were found to act as "rheostats" where some amino-acid substitutions reduced - while others improved - affinity for CO2. No individual point mutation was found to substantially improve the catalytic rate, but a number of highly phylogenetically conserved positions were found to tolerate mutations, indicating that a large portion of rubisco9s sequence space remains unexplored by nature and may serve as a resource for future protein engineering efforts. Together, these biochemical measurements inform our understanding of biochemical tradeoffs and will assist in future efforts to improve rubisco catalytic properties.