A study published a little while back in Nature found an association between shifts in climate (in this case, shifts associated with El Niño) and international conflict. The researchers' hypothesis was that El Niño was messing with people's psyches and also creating economic shocks by tweaking food prices, dredging up storms, and fostering disease. These effects tend to make people a little testy and, boom!, conflict.
But, as Sarah Zielinski writes at Smithsonian, it's too simple to say that climate change will cause war:
[The researchers] also caution that there results “might not generalize to gradual trends in average temperature or particular characteristics of anthropogenic climate change.” … we can conclude from this study that changes in weather patterns can contribute to conflict. … We can also see from these studies that there are no easy answers in this arena. Any conflict — even one as simple as an argument with a neighbor that ends in a fistfight — has a complex set of factors that work together to foster the violence.