The universe may be a deterministic system, but that doesn't mean random chance doesn't exist, or that you can determine the exact path the future will take in advance. For example, Heisenburg's uncertainty principle shows that you can affect an electron's position by measuring its momentum, and vice versa. That's because electrons are so small that the act of observing them causes a change in their position or momentum, depending on whether you're measuring their momentum or position. There's a well-known experiment where you shoot electrons at a double-slit in a screen and then see what pattern they form; if you don't observe the electrons going through the slit, they generate a standard wave interference pattern (meaning the electrons are seemingly interfering with themselves), but if you do, the pattern changes to one generated by particles. Furthermore, if you delay the observation (i.e., by using a removable detector screen), you can cause a retroactive change from a wave pattern to a particle one, and if you make it possible to destroy the measurement of which slit the electron goes through, you can cause a second retroactive change, from a particle pattern to a wave one.
Here's something interesting to think about. Let's say you have two people, essentially identical, except one believes that free will somehow exists, and the other believes that it doesn't. The two people will act differently based on whether they believe in free will or not. Furthermore, if they later change their minds (in other words, make themselves believe the opposite of what they believed before), it will change their behavior. To make the point even clearer, if you had a third person who had never heard of free will, they'd act in a completely different way than the other two - but once they heard of it, depending on whether it was "free will exists" or "free will doesn't exist", it would instantly change their behavior from then on.
In other words, yes, I believe it's possible to change your own behavior by making yourself change what you believe. I don't know whether that would actually be considered free will, but I do know that it's close enough to count for me.