In Game, there is no reference to the CIA to my knowledge. Known parts of the government, and parts believed to exist from extrapolated canon sources can be found here:
http://fallout.wikia.com/wiki/Federal_government
So, with no official answer, we're left with Speculation. Based on the CIA's founding date of 1947 (thanks Wacky-I-Err-mean-WikiPedia), and given that the divergence is believed to happen sometimes in the 1950's, the CIA probably did exist, at the very least, at some point.
If yo want to keep a bit closer to known canon, you may want to consider having a US Army Military inteligence unit, although this might not work for all situations (http://en.wikipedia.org/wiki/United_States_Army_Military_Intelligence might be a good springboard) as we know the US Army definately existed.