Cop an attitude
Adopt an aggressive or antagonistic bearing.
This follows on from previous 'cop' phrases:
Copped it - to be caught or be in trouble, recorded from 1884.
Cop a feel - to fondle sexually, recorded from 1935.
Cop on with - associate with, recorded from 1940.
Cop here is the slang term meaning 'to catch, take hold of, pick up'. This is the most probable source of cop as the slang term for policeman incidentally, that is, copper is 'one who cops'. There's no evidence for the often-quoted 'constable on patrol' acronym as the origin of cop and this is in the same unsupported category as golf and posh. Likewise the story that the term originated because policemen wore copper badges. Nice story, but lacking evidence of any link.
This 'catch' sense of cop has been current since at least 1868, as here from the Daily Telegraph:
"The privileged driver, on dropping his fare almost invariably ‘cops’ a job on his way back."
'Cop an attitude' is later, but is a direct descendent. It's not surprising that the term would have emerged around that time, when the word 'attitude' took on an additional meaning. This is one of those terms, like chic or cool, which don't sound right when defined on the page, but 'you know it when you see it' - something like 'confrontational stylized individualism'.
An early printed citation is from Rolling Stone, April 1975, but again, isn't likely to be the very earliest:
"Natty dreadlocks means hair with an attitude: kinky, jungle thick and matted into tortuous antibraids."
Before long almost anything could be '...with attitude'. Cop had a resurgence then too, with 'cop off with', meaning - to establish a sexual relationship. This is recorded from 1986 and the meaning is well demonstrated in this, from The Face September 1994:
"90 per cent of clubbers go to clubs to cop off, dance their arses off and get out of their head."
With both 'cop' and 'attitude' being heavily used slang terms in the 1980s, it's no big surprise that the first printed citation of 'cop an attitude' is from the Oakland Tribune, February 1976, advertising platform shoes:
"Cop an attitude, with altitude - dressy slip-ons... "
The nature of that reference implies the reader would already be familiar with the term. As street slang, it may well have been in circulation for some time before 1976.