The precession of the orbit of a planet can partially be explained when taking into account the impact of the other planets. Also general relativity is needed to describe this precession exactly. The best known example is the orbit of Mercury. What about the other planets? Is there GR also required?
The difference between the observed precession rate and the calculated precession rate excluding GR is called the anomalous precession. The magnitude of the anomalous precession rate depends mostly on how close the orbit gets to the Sun because the curvature of spacetime decreases rapidly as we move away from the Sun.
So we expect the anomalous precession to be greatest for Mercury and decrease rapidly with distance, and indeed this is what we observe. A quick Google found values for the calculated anomalous precession on page six of this paper on the Arxiv (the precession is in arc-seconds per century):
Mercury 43.0 Venus 8.6 Earth 3.8 Mars 1.4 Jupiter 6.2 × 10−2 Saturn 1.4 × 10−2 Uranus 2.4 × 10−3 Neptune 7.8 × 10−4 Pluto 4.2 × 10−4
The anomalous precession gets immeasurably small for the outer planets, but in principle it is still greater than zero.