“Row”–defined by the OED as “a noisy or violent argument”–is a useful word, being roughly in the middle between “fight,” on the one hand, and “quarrel” or “argument,” on the other.
It is definitely a Britishism–or at least, has been one since about 1930, according to this Ngram viewer chart. (The OED‘s first citation is from 1746.) I searched for the phrase “had a row” to reduce other uses of the word.
My sense is that in recent decades, “row” has generally been limited in the U.S., first, to pretentious people and, second, to headline writers, based on another useful quality: its brevity. However, this sentence appeared recently in the text of a Wall Street Journal article, in reference to a Philadelphia woman: “Mrs. Stokes, 63, was arrested twice in 2008 and 2010 during rows with her now-estranged husband.”
I searched “had a row” on Google News and had to go back about 90 hits before I found one from an American source–a Chicago classical music website. But it turned out to be a quote from a British director. So for now, useful or not, “row” is still “on the radar.”
notoneoffbritishisms.com 
It’s the pronunciation that differentiates the usage, which has long been prominent in the US, as row rhyming with how, as opposed to British row, as in rowing a boat.
I agree with pronunciation differentiating the meaning, at least in the U.S., as that’s been my lifelong experience.
Likewise in the UK: boating “row” rhymes with “know”; arguing “row” rhymes with “how”. So there’s a nice assonance pattern to “we’re rowing about rowing a boat”.
Unless I misread it, the OED lists how-rhyming as the way it’s pronounced in both countries.
Correct. A British row (as in ‘a barney’ or ‘a dust-up’) is pronounced like how. However you could also say row (as in boat) and that would mean exactly that – oars, rollocks etc.
To “headline writers” I would add crossword puzzle constructors.
If you are having a row you are being rowdy. Having a row and being roadie doesn’t really work…
Though there are plenty of rowdy roadies.
I learned the British “row” in context, as a schoolboy in the 1960s. That’s what Flo would have with her ne’er-do-well husband, Andy Capp. The local paper also ran Fred Bassett. I probably learned mot UKish from that strip.
Though ‘row’ is used as a synonym for ‘din’ in Norton Juster’s ‘The Phantom Tolbooth’ (in the chapter where Milo encounters Dr Dischord), which I’d regard certainly as US usage. The book was published in 1961, but maybe isn’t typical.