While Superman is easily one of the strongest characters in any comic book universe, even he can’t break Captain America’s shield. Due to his Kryptonian heritage, Superman has the power to harness the energy from Earth’s yellow sun and transfer that into near godlike powers. The more he is exposed to the sun of Earth’s solar system or any other like it, the stronger Superman becomes, even at one point becoming so powerful that he shattered an entire dimension with a single punch. However, at his base strength, Superman is nowhere near strong enough to break Captain America’s shield.
Captain America’s shield cannot be destroyed by raw strength. The reason that is the case is because the shield is made of a unique vibranium alloy giving it the capacity to absorb any blow no matter how strong the strike is. Whenever someone like the Hulk has tried to attack Captain America by attempting to break through his shield, he has failed, meaning Superman doesn’t have a chance.
Superman in his base form is only a little stronger than the Hulk which was proven in the comic Marvel vs DC #3 by Ron Marz, Dan Jurgens, and Claudio Castellini. In the issue, Superman and the Hulk go head-to-head in a fight that ends with Superman knocking the Hulk out cold. After he was able to take down the Hulk, he said to himself, “He took everything I had, and almost stood up to it. Nothing left now…” proving that Superman is stronger than the Hulk, but only just barely. Throughout Marvel Comics, the Hulk has tried and failed to break Captain America’s shield but has never even come close, and since Superman is only a little bit stronger than the Hulk in his base form, it makes sense that Superman wouldn't be able to break the shield either.
The only way to destroy Captain America’s shield is with cosmic energy or molecule manipulation which has only been shown a few times within Marvel Comics continuity. At one point, Cap’s shield was broken by Thanos when the Mad Titan was wielding the Infinity Gems in the Marvel Comics crossover event Infinity Gauntlet. Another time when the shield was shattered was by Molecule Man, proving true that strength isn’t enough to break the shield and only cosmic or molecular powers do the trick.
When Superman was powered-up enough to shatter a dimension with a single punch as shown in Justice League #25, he would maybe have enough strength to crack Captain America’s shield as, at that point, Superman tapped into a near cosmic energy and thus may be able to pull off the impossible feat. However, Superman with his normal powers from the rays of Earth’s sun isn’t much stronger than the Hulk and therefore cannot break Captain America’s shield.