You couldn’t do it with one slingshot, as several people have explained. But if the slingshot was big enough to launch a ship carrying someone with another slingshot, you’d do a little better. With the second ship carrying a third ship and so on, the slingshot round on the last ship might move fast enough. This is how multi-stage rockets work, by the way.

Added: the math you want is called the Tsiolkovsky rocket equation.