Extreme climate change due to heat-trapping gases, especially carbon dioxide, necessitates its mitigation. In this context, the carbon dioxide sequestration technology of enhanced weathering has for years been investigated, with a possible implementation strategy via alkaline mineral soil amendment being more recently proposed. Candidate materials for enhanced weathering include calcium and magnesium silicates, most notably those belonging to the olivine, pyroxene and serpentine groups of minerals, given their reactivity with CO2 and global availability. When these finely crushed silicate rocks are applied to the soil, the alkaline earth metal cations released during mineral weathering gradually react with carbonate anions and results in the formation of pedogenic carbonates, which, over time, and under the right conditions, can accumulate in the soil. This review paper critically reviews the available literature on alkaline mineral soil amendments and its potential to sequester enough CO2 to be considered a climate change ‘stabilization wedge’. Firstly, evidence of how agricultural soil can serve as a carbon sink in discussed, based on the observed accumulation of inorganic carbon in alkaline mineral-amended soils. Secondly, the impact of alkaline minerals on agricultural soil and crops, and the factors determining the rate of the weathering process are assessed. Lastly, the CO2 sequestration potential via alkaline mineral soil amendment is quantified according to an idealized shrinking core model, which shows that it has the potential to serve as a climate change stabilization wedge.