What planetary orbital anomaly was successfully explained by general relativity?

The planetary orbital anomaly successfully explained by general relativity was Mercury's perihelion precession.

Mercury's elliptical orbit slowly rotates, so the point of closest approach to the Sun—the perihelion—shifts from one orbit to the next. Most of this precession is explained by Newtonian gravitational effects from the other planets, but a small unexplained remainder remained after those influences were calculated.

In 1859, Urbain Le Verrier identified the discrepancy and suggested that an unseen planet, later nicknamed Vulcan, might orbit between Mercury and the Sun. No such planet was found. In 1915, Einstein's general theory of relativity explained the remaining motion as an effect of curved spacetime around the Sun. The relativistic contribution is about 43 arcseconds per century.

The answer is sometimes confused with Mercury's retrograde motion, which is an apparent change in direction seen from Earth and is a normal viewing effect. Mercury is not the only body with relativistic perihelion precession: Venus, Earth, Mars, asteroids, and binary pulsars show the same general phenomenon, though usually more weakly or under different conditions.