You’d have 1/8th the powder charge in a chamber with 1/8th the volume, encased by a barrel 1/2 as thick to contain the same pressure as the full size one.
If you're talking about actually scaling, like a CAD drawing, then no.
If you're talking most of the appearance and function, then yes! There is a scale model of a Browning M2 machine gun (which normally fires 50 cal ammo) that fires 22lr instead. It will set you back about $20,000.
I'm mostly thinking appearance and function, I recognize that rim fire 22lr is absolutely not going to work in a center fire without some sort of conversion.
If you're only after appearance and function then there are plenty of 1911 .22lr or just .22 out there. They look almost exactly like a 1911, yet only fire 22
There is a whole youtube rabbit hole you can go down showing videos of miniature versions of larger (larger caliber) guns. The smallest I saw was "replica" Civil War Navy revolver that the whole gun was about 6cm long. It was a functional gun that had a powder charge with a projectile.
More changes would be needed than direct uniform scaling - .22lr is rimfire, whereas .45acp is centerfire, for example, and their aspect ratios are different. The mass and strength of uniformly scaled-down parts also might not match the recoil and pressure provided by the smaller round, and might result in failure to reliably cycle the action or the gun bursting if the mismatch is too much.
To clarify for the OP, these don't generally scale down the whole gun. Caliber conversions can be as simple as swapping the bolt.
You can also sometimes swap to a larger caliber. They make 'conversion kits' for the AR-15 that are functionally just most of a new gun. You can get those for a variety of calibers from 7.62x39 to .50 Beowulf.