"Cop" is a shortened version of the word "copper." This slang term for police officers is derived from the verb use of "cop," meaning to take, steal or arrest.
In the 19th century, the verb "cop" was used regularly to refer to the arrest of criminals by police officers. Eventually, the police officers were called "coppers," and, later, that was shortened to "cops." Other suggestions for the origins of the term "cop" have little support. For example, "cop" is not an abbreviation for "constable on patrol." It is also not a reference to large copper badges worn by some police officers of the late 19th century.