Possibly the strongest human "fingerprint" on rising CO2 levels comes from the changing ratio of carbon isotopes.
Basically, there are three isotopes of carbon -- carbon atoms with varying weights of neutrons -- carbon-12, carbon-13, and carbon-14. Carbon-12 and carbon-13 are stable and make up most of of the carbon in living things and the atmosphere. (I'm paraphrasing the American Chemical Society discussion.) Carbon-14 is (mainly) created when cosmic rays hit nitrogen atoms in the atmosphere; it's less statable and has a half-life of 5,730 years. All three forms behave pretty much the same in chemical reactions and the environment. Plants and animals use carbon as building blocks and accumulate all three isotopes in their structures.
Things that are alive now accumulate carbon isotopes in the same ratio as they're available in the environment; when plants or animals die, they stop accumulating carbon carbon, and the carbon-14 in their structures breaks down according to its half-life, which is how researchers do carbon dating of ancient materials.
What this means is that very old concentrations of carbon -- such as oil and coal -- contain little or no carbon-14, just carbon-12 and carbon-13. When you burn these materials, the combustion process forms carbon dioxide, and the carbon in those CO2 molecules will be carbon-12 and carbon-13. Thus, you can sample the atmosphere, analyze the mix of isotopes, and determine how much of the CO2 comes from fossil sources.
The rise in CO2 is unambiguously caused by human activity, principally
fossil-fuel burning. This is clear from the numbers: We know how much
fossil fuel is converted into CO2 each year and emitted into the
-- Scripps Institution of Oceanography geochemist Ralph Keeling