This is incredibly tricky, fraught with controversy, and may not be the best way to go. Essentially you have to be assuming that climate is affecting the cultures you are studying archaeologically. This is a fairly safe bet in many circumstances and at a broad scale, but gets very tricky in specifics. At the end of the day, you are probably better off studying the climate change using non-anthropogenic proxies such as pollen or stable isotopes to identify the changes in climate through time, then tie that to any archaeological evidence you may have to show possible impacts of climatic variability on the subject culture(s). 

It is certainly possible to incorporate climate parameters with archaeological findings for this purpose.  The best starting point if you wish to look for examples to follow is the work of Professor Fekri Hassan who has been doing this for decades, I would also suggest looking at Peter deMenocal's work on the North Atlantic Drift.  William Quinn has also done some good work in this field in particular

Quinn, WH (1992) A study of Southern Oscillation-related climatic activity for A.D. 622-1900 incorporating Nile river flood data, in HF Diaz and V Markgraf (eds.) El Nino: Historical and Paleoclimatic Aspects of the Southern Oscillation, Cambridge, CUP.

provides a good, if rather dated starting point.  Indeed I would try to access the whole volume if possible.

However, I must add a cautionary note as Ian says this field is fraught with controversy, I found this when I used such modelling as part of my PhD thesis, the external failed it because of this and I had to remove all such work in order to obtain an MPhil.  Therefore, whether you go ahead may depend on your situation.  You do not mention why you are conducting this research.  If you are hoping to incorporate it into a PhD my advice is don't, the same applies if you are a junior, early career researcher since in my experience it is only established senior academics who can get this sort of research accepted.

If you feel confident in pursuing this approach, however, I can dig out my old doctoral thesis notes and see if there are any more specific references if you let me know which areas you are particularly interested in.

Please log in to Deccan College Pune, India and hope you will get a good idea how archaeological and anthropological date are used to infer climate change.

I agree with Ian's clear answer on this question and Timothy's warnings. Inferring past climate should be a separate research trajectory for comparison with archaeological data. As Ian points out, it is reasonable to infer that climate is affecting past cultures. However, identifying what part of the archaeological record might reflect that is a valuable research goal but hardly straightforward. Certainly there are environmental data from any particular archaeological site that can be evaluated from faunal remains, floral, and geomorphologica/geoarchaeological  investigation of the site formation setting and dynamics, but how that relates to larger scale patterns of climate or climate change (global or even local as may be available from climate science data) is the first hurdle. Determining which artifactual or spatial relationships between archaeological materials might implicate human responses to any inferred "static" climate condition (if such a thing even existed) is daunting, not less trying to link it to changing climate. Even with a stratified site representing a long temporal sequence, it is more than unlikely that the archaeological record represents the debris from equivalent kinds of behaviors to track different human "responses" across those periods of time. Changes in frequencies of remains that can be inferred to be food also will not unambiguously identify differences in resource availability due to climate. For example, it is well know that hunter-gatherers make strategic choices about resource target differences based on a wide number of conditions (not just food avaialbility based on season or larger scale climate considerations), only some of which might even be represented in any particular site.  The links between climate and past human behavior are an important question, but secure inferences will require more rigorous methods and standardized observations than are currently availalbe even from most regional archaeological data sets. This is an important question Isah, but you may need to start small and focus on data that can be very well controlled to first even postulate that there are causal links between climate data and particular archaeological remains. 

Actually Rusty my reservations were not connected with the viability of the research as much as it's reception.  There is a great deal of material available that would make a viable research project, and this is work that it is particularly important that it is undertaken since it provides an opportunity for the historical disciplines to demonstrate their wider relevance to funding bodies by contributing to the concern regarding the impact of climate change.  The problem is that by it's very nature it is going to be multidisciplinary and this can be very hard for early career scholars, whether doctoral, post doctoral or junior academics to get accepted.  A junior scholar lacks the credibility to convince senior colleagues of the viability of their research if it incorporates ideas and fields that said colleagues/supervisors are unfamiliar with.  The risk is then that their career is affected by a negative reaction.

  A related problem is that of the rank of the institution, in your case  Isah you need to think very carefully on how much support his university will give you against external pressure.  This often depends on the relative perceived academic rank of the institutions concerned.  In your case Rusty I suspect that Harvard is well enough respected that this would not be a problem, however, personal experience has taught me that this is not the case when someone from a low ranking institution clashes with an academic from a far higher ranked one.  Their institution will not risk offending their 'betters'.

I regret Isah that I am not familiar with your institution so if I have seemingly offended it please forgive me.  I strongly suggest you talk with colleagues about these issues and see if you can determine whether such issues have arisen before and if so how they were dealt with.

Finally do your best to gain support from people who carry some weight in the academia of both your country and internationally, of the latter I suggest Fekri Hassan Peter deMenecol and Bill Ruddiman, all of whom have produced works in a similar field and have exemplary academic credentials, indeed I suggest referencing the following

Ruddiman, William F. (2008). Earth's Climate, Past and Future (2nd ed.). W.H. Freeman. ISBN 978-0-7167-8490-6

Ruddiman, William F. (March 2005). "How Did Humans First Alter Global Climate?". Scientific American.

Ruddiman, William F. (December 2003). "The anthropogenic greenhouse era began thousands of years ago". Climatic Change. 61: 261–293. doi:10.1023/B:CLIM.0000004577.17928.fa.

as further good places to start