Use lots of photovoltaic power (light) to sequester CO2 and H2O and jam it together into more complex carbon compounds? If trees can do it, we can at least approximate it (trees come from the air, not the ground).
A bio method will likely be a lot cheaper. Algae plastic would be three route to look at as you can grow a ton of algae very quickly. A little GMO and you could optimize it for CO2 sequestration.