We already do this. Consider Las Vegas... its water comes from the Colorado River. (Edit: to be clear, the Colorado River itself is transporting water from areas with high rainfall to areas with low rainfall. The Las Vegas area is a desert, but most of the Colorado River basin is not.)

It's just not generally done over long distances. Oil is pumped over long distances, but it's also much more valuable. For water, we rely more on cheaper ways of transporting it, and transporting it over shorter distances, using things like aqueducts and, yes, pipelines.

Here's an example of a big water pipeline project:

https://en.wikipedia.org/wiki/Northern_Cyprus_Water_Supply_P...