The short answer is no. But the short answer does not often satisfy those who are out to prove the existence of God, so it's important to understand what evidence is, as well as the importance of the burden of proof.
Evidence is verifiable data. It is measurable and observable. An anecdote or gut feeling is not evidence because it is not measurable or observable, therefore it cannot be proven or disproved. A lot of people think that their faith is proof of God, but faith is nothing but a belief not based on proof. It is a voluntary abandonment of rational thinking. When I was a child, I had faith that Santa Claus was going to leave presents under the tree for me. I believed in him, I had anecdotes about him, I was convinced he existed. Was I correct to believe this? If the logic that faith is enough to prove the existence of a being was a sound one, then that would mean that Santa Claus has to exist because I had faith that he did.
If you say that something is true simply because you believe it to be true, you haven't proven anything, you're just begging the question.
By the same standard, holy books and scripture cannot be used as evidence of God. People often say that yes, God does exist because it's written in the Bible. Well, just because something is written in a book does not make it true. In Harry Potter and the Sorcerer's Stone, Harry Potter is a gifted student of wizardry at Hogwart's Academy -- is this proof that there is indeed a boy named Harry Potter that can cast spells with his wizard wand?
Of course Harry Potter was not written as non-fiction as the Bible and other holy books were, so we must also consider the abundance of inaccuracies and inconsistencies found in scripture. One simple example of this is the obvious lack of basic scientific awareness found in holy books. The men that wrote these books did not know that the earth revolved around the sun, they all thought it was the other way around. If they were truly inspired by a divine, omnipotent God, don't you think they would have at least been clued in as to how God's universe operates?
People often defend the existence of God by saying that there is no evidence that he doesn't exist. This is a logically fallacy as well. The burden of proof is on the person making the claim, not the person questioning it. For example, what if I told you that I have an invisible purple unicorn living on my roof right now? Is it my job to prove its existence, or yours? If it's your job to prove that I don't have an invisible purple unicorn living on my roof, how exactly are you going to do that, considering it's invisible? Using this false logic can lead to all kinds of absurdity because one cannot disprove something that does not exist.
So, as it is now, there is no evidence that God does exist. Does this mean that He absolutely does not exist? Absolutely not. It just means that He has yet to give us conclusive evidence that He does. We can always keep questioning though.