It is possible, here is the Wikipedia article on it. You do have to check that the plastic in the waterbottle doesn't prevent the UV light peneatrating the bottle.
Some glass or PVC materials may prevent ultraviolet light from reaching the water. Commercially available bottles made of PET are recommended. The handling is much more convenient in the case of PET bottles. Polycarbonate (resin identification code 7) blocks all UVA and UVB rays, and therefore should not be used. Bottles that are clear are to be preferred over bottles that have been colored. For example: the green of some lemon/lime soda pop bottles.
It doesn't work if the water has lots of particles.
If the sunlight is less strong, due to overcast weather or a less sunny climate, a longer exposure time in the Sun is necessary.
It also doesn't work if there are lots of particles in the water.
When the water is highly turbid, SODIS cannot be used alone; additional filtering or flocculation is then necessary to clarify the water prior to SODIS treatment
I don't know if it would purify stream water because it is moving, but I have heard that it will purify very high, shallow alpine lakes. One would expect that this method would work better at higher altitudes because of how much more intense the UV rays are.
Personally I have known about this method for a while, but have never used it, mostly because I didn't want to wait around it to work. I have thought about doing it with clear bottle that are left in camp while one is submitting, so that on your return you would have a bunch or water ready to go.