West African savannas are experiencing rapid land cover change that threatens biodiversity and affects ecosystem productivity through the loss of habitat and biomass, and carbon emissions into the atmosphere exacerbating climate change effects. Therefore, reducing carbon emissions from deforestation and forest degradation in these areas is critical in the efforts to combat climate change. For such restorative actions to be successful, they must be grounded on a clear knowledge of the extent to which climate change affects carbon storage in soil and biomass according to different land uses. The current study was undertaken in semi-arid savannas in Dano, southwestern Burkina Faso, with the threefold objective of: (i) identifying the main land use and land cover categories (LULCc) in a watershed; (ii) assessing the carbon stocks (biomass and soil) in the selected LULCc; and (iii) predicting the effects of climate change on the spatial distribution of the carbon stock. Dendrometric data (Diameter at Breast Height (DBH) and height) of woody species and soil samples were measured and collected, respectively, in 43 plots, each measuring 50 × 20 m. Tree biomass carbon stocks were calculated using allometric equations while soil organic carbon (SOC) stocks were measured at two depths (0–20 and 20–50 cm). To assess the impact of climate change on carbon stocks, geographical location records of carbon stocks, remote sensing spectral bands, topographic data, and bioclimatic variables were used. For projections of future climatic conditions, predictions from two climate models (MPI-ESM-MR and HadGEM2-ES) of CMIP5 were used under Representative Concentration Pathway (RCP) 8.5 and modeling was performed using random forest regression. Results showed that the most dominant LULCc are cropland (37.2%) and tree savannas (35.51%). Carbon stocks in woody biomass were higher in woodland (10.2 ± 6.4 Mg·ha−1) and gallery forests (7.75 ± 4.05 Mg·ha−1), while the lowest values were recorded in shrub savannas (0.9 ± 1.2 Mg·ha−1) and tree savannas (1.6 ± 0.6 Mg·ha−1). The highest SOC stock was recorded in gallery forests (30.2 ± 15.6 Mg·ha−1) and the lowest in the cropland (14.9 ± 5.7 Mg·ha−1). Based on modeling results, it appears clearly that climate change might have an impact on carbon stock at horizon 2070 by decreasing the storage capacity of various land units which are currently suitable. The decrease was more important under HadGEM2-ES (90.0%) and less under MPI-ESM-MR (89.4%). These findings call for smart and sustainable land use management practices in the study area to unlock the potential of these landscapes to sequestering carbon.