This isn't really a historical question, as we don't have records from before the invention of agriculture, so /r/AskAnthropology might be better.

However, for the sake of using history to answer this question...

In historical times there've been a number of cultures that don't use agriculture- we call them foragers or sometimes hunter-gatherers. It just so happens that foragers vary a lot on war- some such as the San and Hadza, though they would have things like homicide, didn't historically engage in war except with non-forager outsiders, while others, such Australian Aborigines and Pacific Northwest Indians, are well known for their warrior traditions. Given that a lot of foragers did have some kind of war, it's a safe assumption that war predates agriculture.