Not water (H2O) per se, at least not as a single propellant, but as a reaction mass, propellant component (ALICE is a rocket propellant that consists of nanoaluminium powder and water, both mixed in ice form to keep it stable), or atomic components of water molecules that we could separate with the use of electrolysis and producing diatomic oxygen (O2) as an oxidizer and a diatomic hydrogen (H2) as fuel, sure that would work and components of water molecules are already used in many launch systems, albeit in their cryogenic liquid state to increase their density.
ALICE has specific impulse (Isp) of 210 seconds in theory, in practice though closer to 150 seconds, which is really not that much compared to cryogenic LOX/LH2 with specific impulse (both at sea level) of 391 seconds, and it also requires an additional propellant component (nanoaluminium powder) to be taken onboard, so it wouldn't be the most suitable for missions to distant celestials that require refueling. But in case of both using water as a reaction mass that you could expel at your engine exhaust and produce thrust, for example with the use of ion thrusters, or by separating molecular water into its constituent components and use that as your source of oxidizer and fuel components of your propellant, it doesn't require additional propellant components, but it would require strong source of electrical power.
Lucky for us though, taking onboard either Radioisotope Thermoelectric Generators (RTGs) or later relying on Photovoltaic Arrays (where the source of light radiation is more or less continuous and strong enough, i.e. in the inner Solar system) provides for relatively light, strong and long duration energy source (RTGs), or sustainable source of it, where it's readily available and merely need collecting (Solar Arrays). There are, of course, other ways of producing electrical power.
So, to recap:
- Use molecular water as your reaction mass, for example with ion thrusters that could greatly accelerate its molecules as ions and plasma on the engine's exhaust and produce thrust, or
- Use electrolysis and separate water molecules into its constituent atomic components, oxygen and hydrogen, and use that as your oxidizer and fuel components to your bipropellant
For pure water in its liquid state, electrolysis requires a minimum voltage of 1.229 V (Volt) and separates H2O into negative oxygen ions (anions) at its positive anode, and positive hydrogen ions (cations) at its negative cathode ends as atomic ions that combine into diatomic gas, H2 and O2, respectively:
$$2H_2O → 2H_2 + O_2 -1.229 V$$
These two oxidizer and fuel components in gas form could then be compressed and stored in their cryogenic liquid form for later use with cryogenic liquid propellant rocket engines. Such techniques could serve both for refueling stations, or be done onboard your spaceship itself.
Taking either strong electrical power sources or having solar panels onboard is still a lot cheaper in terms of your requirements to accelerate to required delta-v to reach escape velocities of whichever celestial body you'd like to make a distance from, than having to also take all your reaction mass with you.
So having readily available sources of this reaction mass your rocket will be using to produce thrust and propel itself, be it on spaceship's own accord, or with the use of separate refueling stations, is imperative to our endeavours of exploring distant places and keep economy of it manageable, something we could afford on a larger scale.