What is the time-lagged correlation between historical $\ce{CO2}$ records from ice cores and global temperature records?
From wikipedia:


  
  Studies of the Vostok ice core show that at the "beginning of the deglaciations, the CO$_2$ increase either was in phase or lagged by less than ~1000 years with respect to the Antarctic temperature, whereas it clearly lagged behind the temperature at the onset of the glaciations".$^{[1]}$ Recent warming is followed by carbon dioxide levels with only a 5 months delay.$^{[2]}$ The time lag has been used to argue that the current rise in CO$_2$ is a result of warming and not a cause. While it is generally agreed that variations before the industrial age are mostly timed by astronomical forcing,$^{[3]}$ a main part of current warming is found to be timed by anthropogenic releases of CO$_2$, having a much closer time relation not observed in the past (thus returning the argument to the importance of human CO$_2$ emissions). Analysis of carbon isotopes in atmospheric CO$_2$ shows that the recent observed CO$_2$ increase cannot have come from the oceans, volcanoes, or the biosphere, and thus is not a response to rising temperatures as would be required if the same processes creating past lags were active now.$^{[4]}$
  



Historical carbon dioxide record from the Vostok ice core - Carbon Dioxide Information Analysis Center, 2003.
Spencer R. Weart, 2006, The Discovery of Global Warming
Kuo et. al., 1990, Coherence established between atmospheric carbon dioxide and global temperature
More Notes on Global Warming - Physics Today, 2005