Absolutely. In fact, our oldest sources from ancient Iraq, the FIRST written records we have, talk about a dispute between two city states, Umma and Lagash, about rights to the Tigris river for irrigation and farming reasons, as one city was farther upstream and they had a growing rivalry, so they would take it upon themselves to divert much of the flow of the river and use as much as they could to reduce the flow by the time it got to the lower city, Lagash.

The Stele of the Vulture was erected to commemorate the Lagashite victory.

http://en.wikipedia.org/wiki/Stele_of_the_Vultures

Interestingly enough, in addition to water rights, the war was kicked off by Umma not withholding its end of the bargain in paying Lagash to use some of their land for farming with their workers, and they owed them crops. Things got out of hand, water was diverted, and the Lagashite King marched north (with some sort of foreign mercenary force to swell his ranks), and defeated the Ummaites, and reduced the amount of land they had to work, and increased their Tithe in the following years.

Source: Jerrald S. Cooper, Documents in Translation, the Umma-Lagash Border Conflict

http://cdli.ox.ac.uk/wiki/doku.php?id=umma_lagash_border_conflict

http://www.thenagain.info/classes/sources/ummalagash.html

Also of note is that this is in the Early Dynastic III Period, roughly 2600-2350 BCE.