'just got around' is correct and usable in written English.
It is an idiom that means 'finally accomplished; began to do something.' For example: "I finally just got around to calling my grandmother; I hadn't spoken to her in months."
Depp's agent had only just got around to telling the actor the exact figure he would earn for starring in The Man Who Killed Don Quixote.
Last book I loved: I know everyone has already read Michael Lewis's "The Big Short," about some of the individuals who cashed in betting on the financial collapse in 2008, but I just got around to it.
It's fine for those who stockpile swimwear and sandals at the first sighting of a swallow, but what about those of us who have only just got around to booking a holiday?
It turned away too many Jewish would-be refugees at its borders; indeed, it has only just got around to pardoning those Swiss citizens who illegally helped Jews to enter the country during the Nazi period.
The band have only just got around to releasing an album but - thanks to word of mouth, the web and the enterprising Vortex Jazz Club - its young fans already know their tunes by heart.
I instantly downloaded it but have only just got around to listening: as the title suggests, it's a career-spanning collection mixed and slightly reworked by DJ X-Rated and DJ Esco, taking in solo work, Outkast efforts and some of his guest appearances.
"The Boondocks," meanwhile, was just getting around to discussing "The Passion".
Three years later, I'm just getting around to sharing those words, and regret their relevance.
She's just getting around to it, and in the interim, she's been dealing with a bunch of losers.
"Just getting around can sometimes be a bore," conceded Miss Lambert, who does not travel more than a city block without a limousine.
"I'm 54 now, but I feel that I'm just getting around to distilling what it is I want to say musically," he said.
