There are any number of organisations involved in in capturing and storing carbon. 
Most are involved with engineering solutions and others are investigating nature-based solutions (NbS). 
However, although there are a number of organisations involved in sequestering carbon with cacti, they are not considered NbS!

The most likely cactus is Opuntia since it provides many benefits in the dry lands where it is normally grown. 
Some is grown in Africa but there is an enormous area where it could be found since over half the land is unsuitable for normal crops!

If there is a choice to be made as to what to grow for carbon sequestration there is no competition. Opuntia absorbs about10 times that for the same area of trees!

Even better, when any cactus plant dies unlike trees it does not release carbon dioxide! I? Instead the 'leaves' and stalks turn into a chemical that eventually turns into calcite (calcium carbonate)! This is gradually pushed down into the soil/sand and becomes part of a deep carbon store! 

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Using Bamboo to capture carbon dioxide

Bamboo not only grows fast but captures CO2 quicker than trees!                                                                                       And, unlike cacti, grows nearly everywhere - some even in deserts!