Final answer:
Uranus is the planet that has a rotation axis perpendicular to its orbital plane, causing it to orbit on its side.
Step-by-step explanation:
The planet that orbits on its side, with a rotation axis perpendicular to the plane of its orbit, is Uranus.
This unique tilt means that Uranus essentially spins on its side relative to the other planets, exhibiting the strangest seasons of all the giant planets.
The spin axis of Uranus is tilted by 98° with respect to the ecliptic, which means that during its orbit, one pole or the other is pointed almost directly at the Sun, leading to extreme seasonal variations.