The ice core data does not have enough time resolution to easily address this.
There is a sound physical reason for this.
The oceans are buffers and sources of stored heat. As the earth naturally warms from emerging out of an ice age, this stored ocean energy also begins to heat the atmosphere and then its ability to store CO2 increases.
This is particularly evident if you look at the period from 12,500 to 11,000 years ago.
So the ice core data seems to be telling us that CO2 buildup follows atmospheric warming and does not cuase it.
But, that doesn't mean anything today! Look at the slope of the red line today (far right of the graph). The rate of build up is unprecendent and could certainly reverse the situation where CO2 does produce warming.
This is the most important science message.
Rates matter. Qualitative conceptions don't.