Scientifically, no -- but it can be diluted. Grammar-wise, yes -- but it's seen as an action.
When water (or any other liquid) is placed on something, it had made that object wet. But if water is placed on water, it's just water. It's not wet in that way.
Now, if you place another liquid within water, or water within another liquid, it's just dilution. You're taking out the excess/concentration of the liquid (be it water or something else), but it's not wet.
For it to be wet scientifically, it has to easily be separated or dried. Example -- a wet towel. It has water in it. So it needs to be dried to not be wet anymore.
But when water is combined with another liquid, it's not as easy to separate or dry. If you strain the combined liquids through a strainer, they will still be together (unless it's oil or something similar). If evaporation happens (liquid's equivalent to "dried"), they're likely to evaporate together (unless it's oil or something similar).
Now, if you're talking about "the water has wet the towel" in terms of grammar -- THEN it's wet. Because "wet" in this case is used as an action. The water is doing an action towards the towel, which is "wet".