"The Merriam-Webster New Book of Word Histories says: "Around the year 1700, the slang verb cop entered English usage, meaning 'to get ahold of, catch, capture.' By 1844, cop showed up in print, and soon thereafter the -er suffix was added, and a policeman became a copper, one who cops or catches and arrests criminals. Copper first appeared in print in 1846, the use of cop as a short form copper occured in 1859.""
"To cop" may come Dutch kapen = "to steal"; Irish ceap = "Stop, catch, seize, control", or Old French dialect caper = "to take", from Latin
capere.
Oxford Dictionary of English Etymology
"Cop (sl.) Catch; capture. XVIII. Of north. dial. origin; prob. variant of cap
arrest, seize (VVI) - OF. caper seize - L. capere (see Capture) Hence cop and
copper policeman, XIX. (Oxford Dictionary of English Etymology, p. 213,
Oxford, 1978.)"