We use an ocean-atmosphere general circulation model coupled to land and ocean carbon models to simulate the evolution of climate and atmospheric CO2 from 1860 to 2100. Our model reproduces the observed global mean temperature changes and the growth rate of atmospheric CO2 for the period 1860--2000. For the future, we simulate that the climate change due to CO2 increase will reduce the land carbon uptake, leaving a larger fraction of anthropogenic CO2 in the atmosphere. By 2100, we estimate that atmospheric CO2 will be 18% higher due to the climate change impact on the carbon cycle. Such a positive feedback has also been found by Cox et al. <2000>. However, the amplitude of our feedback is three times smaller than the one they simulated. We show that the partitioning between carbon stored in the living biomass or in the soil, and their respective sensitivity to increased CO2 and climate change largely explain this discrepancy.