Well, for starters, how do you define God?
In order to study something, you have to define what it is. The problem in this case is that today, everyone has his own personal definition of god, what he can and cannot do, his attributes, etc. So, the question isn't "Can science refute God?" but "Can science refute this particular god?".
There is just no possible way to refute all gods because a non-existing entity can always be defined after refutations are done, in such a way as to barely escape refutation. Some gods cannot be refuted to begin with, because they actually do exist. For example, some people claim that god is nature. Nature, certainly exists.
Now, a god such as the god of Christianity, a god which supposedly interacts and has interacted in history, should leave evidence of his existence. The more god is supposed to interact, the easier it should be to prove his existence.
For example, if I claim Unicorns exist in front of my house, it's pretty easy to go there and find them or not. The "You can't prove a negative" is all good until you make an actual material claim. If I say God answers prayer and prove that prayers do nothing, then I've proved that God, if he exists, doesn't answer prayers.
Now, to be consistent, if I define God to:
- Answer prayers
- Intervene in history
- Be all powerfull
- Hold atoms together
If I prove any of those to be false, I have positive evidence against the existence of God. Redefining god or saying "Well, maybe god exists but he doesn't answer prayers" isn't a valid move, becuase of what I said previously.
So yes, God can be refuted by science, and, science does indeed refute the existence of some of the more popular definitions of god.