I mean, when talking broadly, sure you can call water wet. So many people do that!
However, when talking technically, water – or any liquid for that matter – isn’t wet per se. It is a wetting agent.
For instance, when in solid form, do you call ice as “dry water”? Or, when it has evaporated, do you call that as “dried water”?
Water isn’t wet. It has the wetting capacity. If you touch it, your fingers get wet. Wetness is more of an experience.
(Courtesy: Chemistry World)
Rainwater isn’t wet. It has the wetting capacity. This is why when you get drenched, you say “I got wet in the rain”. You don’t say “I got wet in the wet rain”, do you?
In short, water is something that makes other things wet. It itself isn’t wet.
If you’re looking for some term to define it, you can state water as slippery.
Hope this answered your question!!