Could The US Military Defeat One Imperial Star Destroyer?

On the terms most people imagine the fight, yes. If an Imperial Star Destroyer were foolish enough to descend into Earth's atmosphere, the US military would likely make short work of it, because nuclear missiles are powerful enough to break its shields and blow it apart. The problem is that the Empire would never fight that way. It would stay in orbit, outside the reach of anything that can be launched at it, and run a Base Delta Zero. (The Empire Strikes Back)

What a single Star Destroyer actually is#

Start with scale, because the mental picture people carry tends to be off in both directions. (Star Wars: Dawn of Rebellion: The Visual Guide)

The Imperial-class Star Destroyer is 1,600 metres long. Over a mile and a half of dagger-shaped warship. Despite that size it was no rare flagship: the films show whole squadrons of them hunting a single rebel fleet. (Star Wars: Dawn of Rebellion: The Visual Guide; The Empire Strikes Back)

Worth keeping in perspective how far up the ladder that is not. The Executor-class Star Dreadnought ran 19,000 metres and carried over 5,000 turbolasers. A single Imperial-class is one of the routine units the Galactic Empire parked over a world to keep it in line. (Star Wars Encyclopedia of Starfighters and Other Vehicles; Star Wars: The Rebel Files)

The thing that made it a threat to planets was never a superweapon. It was position. (The Empire Strikes Back)

The atmospheric fight is the one Earth wins#

The video's opening scenario is deliberate, and it is right. Bring the Star Destroyer down inside the atmosphere and you have handed away everything that makes it dangerous. (The Empire Strikes Back)

A ship in atmosphere is inside the operational envelope of ground-launched weapons. It is a 1,600-metre target that cannot dodge, at an altitude where warheads can reach it. Nuclear missiles are enough to bring down its shields and destroy it. (Star Wars: Dawn of Rebellion: The Visual Guide)

There is precedent for large capital ships being killed by comparatively small attacks. At Endor, with its bridge shield already knocked out, the 19,000-metre Executor was brought down when a single crippled A-wing crashed into its bridge. Big warships have soft spots and known weak points. (Return of the Jedi)

The catch is that this is a scenario the Empire would have to volunteer for. (The Empire Strikes Back)

Base Delta Zero is the fight Earth loses#

The Imperial answer to a hostile surface is not to land on it. It is Base Delta Zero: sustained orbital bombardment, continued until the target is stripped. (The Essential Guide to Warfare)

In the Legends continuity, Star Destroyers could render a planet lifeless this way without destroying the planet itself. Unlike an actual superweapon, it took time, usually more than one ship, and a world with its shields down or sabotaged. (The Essential Guide to Warfare; Specter of the Past)

It got used. In Legends, after a three-month campaign on Milagro, the Empire bombarded the planet rather than let its manufacturing facilities fall to the New Republic. Earlier, in the early years of the Empire, Caamas was bombarded until its surface was dead after its planetary shields were sabotaged, an atrocity that caused a political firestorm decades later when the details came out. (The Essential Guide to Warfare; Specter of the Past)

Current canon has its own example. During the Clone Wars, Separatist forces bombarded Humbarine, a Core World with a seat in the Senate, from orbit and left it utterly seared. (Star Wars: Dawn of Rebellion: The Visual Guide)

Against that, Earth has no answer. The US has no weapon built to hunt a warship holding high orbit, and the Star Destroyer never has to come lower. It would soon annihilate Earth's defences from a position nothing could reach. (The Empire Strikes Back)

The one thing that changes the equation#

There is a defence that works in Star Wars, and Earth does not have it: planetary shields. (The Empire Strikes Back)

At Hoth, Admiral Ozzel's mistake gave the Rebels warning, and they activated the deflector shield protecting Echo Base in time. That single move made orbital bombardment impossible. The Empire had to disembark troops beyond the shield's range and send AT-ATs overland to destroy the generator, which is the only reason there was a ground battle at all. (The Empire Strikes Back)

That is the whole shape of planetary warfare in the setting. If you can raise a shield, the fleet in orbit is neutralised and has to come to you. If you cannot, the fleet never needs to come to you at all. (The Empire Strikes Back)

Earth cannot raise a shield. So the Empire keeps the range advantage indefinitely. (The Empire Strikes Back)

The honest verdict#

The question splits cleanly in two. (The Empire Strikes Back)

Can the US military destroy an Imperial Star Destroyer? Yes, if the ship enters the atmosphere and stays there long enough to be hit. That is a real vulnerability and Star Wars capital ships have died to less. (Return of the Jedi)

Can the US military defeat an Imperial Star Destroyer? Not on the Empire's terms. Winning requires the enemy to fight badly. Any competent Imperial captain sits in orbit, waits, and burns the surface at leisure while nothing fired from below gets anywhere near. (The Empire Strikes Back)

The only Star Destroyers that lose to a planet are the ones commanded by someone who decides to come down and have a look. (The Empire Strikes Back)