It is short for copper, but not the metal.
“To cop” means “to arrest or detain” someone. So a “copper” is someone who cops people.

You may be familiar with the phrase “that’s a fair cop”. Which would be an admission that the arrest is fair.

i read that it’s from the archaic verb “cop” which means “to seize”, so the old brits used to call them coppers, then that got shortened to cop, and it’s still in use today.