No, water does not have a texture. Water is held together by electrostatic bonds. At the smallest scale there is the single H₂O molecule. There are strong chemical bonds between the oxygen and the Hydrogen. There is sharing of the lone electron in H with the outer electron shell of Oxygen. Then between the water molecules there is a weaker Hydrogen bond between the Hydrogen of molecule 1 and the Oxygen of a different H₂O molecule. This is called hydrogen bonding....but the word texture does not really apply.

Water certainly does have texture in the sense that despite appearing smooth on the surface, liquid water is made up of billions of water molecules that jiggle and slide past one another in a chaotic molecular dance. If you looked very, very closely you would see a very rugged surface to the droplet. There is a nice Molecular Dynamics simulation on Youtube that gives you a view of water at this scale:
click here
Hope this helps!

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