The full OED has 12 completely separate entries for cop (8 nouns, and 4 verbs). The sense of OP's cited usage derives from these definitions within the Verb 3 entry...
1 to cop verb, dialect/slang - to capture, catch, lay hold of, ‘nab’
...leading to the phrasal verb...
2 to cop it - to ‘catch’ it, to be punished, get into trouble
...and thence to...
3 to cop a plea
a: to plead guilty, usu. as part of a bargain or agreement with the prosecution
b: (U.S. Black English slang) to avoid telling the truth, be evasive.
Although not explicitly noted by OED, 3a is increasingly used without a plea. It's important to note that the underlying "courtroom bargaining" sense there implies plead guilty to a lesser offence (than the one you're really guilty of, but which the prosecution don't think they can prove).
Note the Macmillan definition in @snailboat's comment: to admit to something embarrassing. It's usually a somewhat facetious usage, in that the speaker (more often, writer - a columnist, blogger, etc. wishing to inject an informal/lighthearted tone into his text) doesn't usually think he's admitting to anything that's actually wrong. It's more likely he's gently poking fun at those who might criticize his action (and implicitly inviting his readers to share his perspective), so it's actually more a form of "inverted boasting" - some people might disapprove, but not the writer (or sympathetic readers).
Given that sense 3b above is almost the "opposite" of 3a (superficially, at least), I would advise caution in using it. Outside of the courtroom context, sense 2 is far more common, and I suspect most people would understand OP's cited usage as being facetiously based on that (implying that the "crime" admitted to is either trivial or not actually "wrong" at all).