Other commenters here have given some great answers. The answer is a pretty resounding: No. There is nothing to indicate that "free will" exists, and in fact it is not clear how such a thing even could exist in a universe which operates according to a set of physical laws.
That being said, this is really a moot academic point. For all practical intents and purposes we have no choice but to live our lives and organize our societies as though we had free will. Socially speaking this is a necessary pretense, otherwise nothing would get done.