Well, that depends on what you mean by "taking water to space." Do you mean in a spaceship? That is, is the water exposed to vacuum or not? Let's talk about each case separately.

If the water were exposed to the vacuum of space, it would instantly begin to boil. That's because the molecules in the water are constantly jiggling around - if the water is exposed to air, some molecules move from the water into the air, but some water molecules in the air move back into the water, leaving the water in equilibrium with the air. In vacuum, however, any water molecules that leave the water just float away, so the water evaporates. If the water is weightless, the lack of any pressure makes this evaporation happen throughout the water (and not just on the surface), making it boil. Eventually, this boiling would remove enough heat from the water that some of it would freeze into a chunk of ice. In this case, the density of the water vapor will be much lower than the density of the liquid water (in fact, as water vapor spreads out into the vacuum, its density goes to zero). The density of the ice would be a bit less than the density of the liquid water, too, since ice is less dense than water.

If instead the water is exposed to air but were weightless (as it would be in, say, an orbiting spaceship), then the density of the water would be pretty much the same as it would be on the surface of the earth. Technically, that's not quite true - on the surface of the earth, a glass of water has weight, and that weight "squishes" the water a little bit. The amount of "squishing" is what we call the compressibility of water. In a weightless environment, this squishing wouldn't occur, and the water would be slightly less dense. However, the compressibility of water is very low, which means that the water doesn't squish very much under its own weight; as a result, its density in space would be more or less the same as on earth.

I hope this helps to answer your question!

The density of any substance depends on the pressure and Temperature. The pressure in space is essentially zero and the T is 20 K... so we can take H₂O in lab, put it under these conditions (it would be ice) and measure its density... it would be around 1020 kg. m³ or 1.02 gm/cc

Liquid water, being liquid, would not appreciably change density if moved into a vacuum. However, there is no temperature at which liquid water is stable in a vacuum, so it would immediately begin to boil and escape into space.