Marriage vows for fabric? - Do you, piece of fabric, wish to be joined together with this piece of fabric… 
The only way I can imagine it being pronounced with an ‘a’ sound is in New England, as in, “Pahk the cah, you twaat”
“Twat did you say? I cunt hear you. I have an ear infucktion.”
I hate to say this but we had this same little ditty when we were young but it had a 4th part, “Scum closer”.
I always assumed it rhymed with swat.
So many people talking past each other.
It rhymes with cat in the UK.
The way many people in the UK pronounce “cat” [kat], it sounds more like the American “cot” [kɔt] than the American “cat” [kæt], even though it’s really a third vowel.
So for an American, depending on dialect, rhymes-with-cot might be closer (but will still sound like “twot” to a British person) than rhymes-with-cat.
Does it depend on whether you’re talking about Twatt, Orkney or Twatt, Shetland?
Several Brits saying “cat” a lot.
Please refer to the parting conversation between Hedley Lamarr and Lili Von Shtupp in the venerable cinema classic “Blazing Saddles”
Cot all the way.
Hmmm, the two times I can think of off the top of my head of a British person saying “cat”, they pronounce it as cæt. Actually I was completely sure of this before I double checked just due to my sound memory alone. However, one of these examples he pronounces it both ways, first as cæt and then as a more intermediate cat… phenominal cat by the Kinks.
The other example however that comes to mind was even better than I had remembered. Not only does Syd Barrett distinctively say cæt several times in Lucifer Sam, but the chorus even goes “that cæt’s something I can’t explain”, when most Americans pronounce both words with an æ.
Twat and Twot were two distinct terms when I was growing up;
Twat being the term to describe an annoyingly stupid person (often a determinedly or viciously stupid one)
Twot was more like an equivalent for ‘dork’ or ‘doofus’ - a person whose stupidity was ingrained, but sort of hapless in nature.
If you’ve only ever heard it written and not spoken, you must not watch a lot of British comedy. In British spoken vernacular / comedy the word seems ubiquitous to me. Pops up a lot in Gervais/Merchant stuff. Written out, I see it used liberally by the many British rock musicians who I follow or am friends with on Facebook. In the British spoken pronunciation it (the sound of the ‘a’ in the word) simply varies depending on the wide variation of British accents.
Looks better with a question mark.
Twat?
if you are unsure about how to pronounce it, go for the far more colourful ‘twunt’ - a mix of 2 fabulously offensive words 
I usually think of it as two different words: “twot”, which is a vulgar slang for a woman’s genitalia and “twatt”, which is a mildly rude British insult.
From two experts on culture and good taste, the definitive opinion.
I am not sure where you’re getting this. British “cat” is /kaet/, not /kat/. American “cot,” at least in my dialect where we don’t merge “caught” and “cot” is /kɒt/. /kɔt/ is “caught.”
For more examples, listen to the UK speakers here.
I’m not sure I’ve ever said the word out loud. When I read it in my head I hear something in between awt/ot sound.
I had a same-themed discussion yesterday at work about “pecan.”
Previous post eaten.
Twat rhymes with “cot”. Fighting words where I grew up in Norcal circa 1070’s. As in “your sister is a twat” could not possibly be left uncountered. One of Pat Conroy’s books, IIRC “The Prince of the Tides” has a pretty stereotypical scene where a fist fight is goaded on by those exact words “your sister is a twat”.
Here’s the Forvo page with 10 different speakers pronouncing “twat.”
The first link, UK, it’s /twaet/. Rhymes with “cat.”
The second link, Spanish speaker, it’s something like “twot.”
The third link, Australian, it’s “twaught” or something like /twɒ:t/, with a deep “aw” sound.
Fourth link, American, it’s “twot.”
Fifth link, UK, /twaet/ like “cat.”
Sixth link, UK, /twaet/ like “cat,” although his /ae/ sounds slightly more open to my ears
Seventh link, UK, also sounds like /twaet/ as in “cat” to me, but also slightly more open
Eighth link, US, /twɑt/, rhymes with American “hot”
Ninth link, Australia, sounds like the previous Australian to me, with an /ɒ/ or similar vowel like /ɔ/.
Tenth link, UK, /twaet/ rhyming with “cat.”
Looks like all the UK pronunciations are /ae/ to my ears, though some may be slightly shaded towards /a/.
Australians look like they like something like /ɒ/ or /ɔ/ as the vowel there (“aw”)
Americans look like they like to rhyme it with “hot” /ɑ/
I’m hereby adding “twunt” to my vocabulary and am on the lookout for the 1st available opportunity to use it.