Is there any evidence that Jupiter has had any effect on our polar axis?
Yes, Jupiter is having a continual effect on Earth's axis of rotation.
The Earth's axis of rotation is undergoing nutation which has two components, the precession of the equinoxes and the changing axial tilt. This nutation is caused by the gravitational pull of the Sun, Moon and the other planets. As Jupiter is the largest planet in the solar system, its gravitational pull has a measurable effect.