XKCD, the brilliant and hilarious on-line comic, attempts to answer the question
The answer is, enough to cover the Earth with 10 layers of soda cans. However, the comic misses a factor of about two, which would arise from the ocean. The oceans have been taking up carbon throughout the industrial era, as have some parts of the land surface biosphere. The ocean contains about half of the carbon we’ve ever released from fossil fuels. We’ve also cut down a lot of trees, which has been more-or-less compensated for by uptake into other parts of the land biosphere. So as a fraction of our total carbon footprint (fuels + trees) the oceans contain about a third.
At any rate, the oceans are acting as a CO2 buffer, meaning that it’s absorbing CO2 as it tries to limit the change to the atmospheric concentration. If we suddenly pulled atmospheric CO2 back down to 280 ppm (by putting it all in cans of soda perhaps), the oceans would work in the opposite direction, to buffer our present-day higher concentration by giving up CO2. The land biosphere is kind of a loose cannon in the carbon cycle, hard to predict what it will do.
Ten layers of soda cans covering the whole earth sounds like a lot. But most of a soda can is soda, rather than CO2. Here’s another statistic: If the CO2 in the atmosphere were to freeze out as dry ice depositing on the ground, the dry ice layer would only be about 7 millimeters thick. I guess cans of soda pop might not be the most efficient or economical means of CO2 sequestration. For a better option, look to saline aquifers, which are porous geological formations containing salty water that no one would want to drink or irrigate with anyway. CO2 at high pressure forms a liquid, then ultimately reacts with igneous rocks to form CaCO3.
Tans, Pieter. An accounting of the observed increase in oceanic and atmospheric CO2 and
an outlook for the Future. Oceanography 22(4) 26-35, 2009
Carbon dioxide capture and storage IPCC Report, 2005