The American Crime Story star dishes on her newfound friendship with the 30-year-old singer on Monday's episode of The Ellen DeGeneres Show.
When asked if the two "became friends," Paulson tells DeGeneres, "I like to think [we] did. I'm not sure. I think we're friends," adding that she and Rihanna "have texted."
The 43-year-old actress does admit that it was quite the challenge "to not embarrass" herself in front of the cool GRAMMY winner, stating she would often break into song around her co-star while on the Ocean's 8 set.
"It was a daily struggle to not embarrass myself because every time I looked at her. I was like, 'Work, work, work, work, work,'" Paulson quips, referencing Rihanna's 2016 hit single, "Work."
She adds that their other co-star in the crime thriller, Sandra Bullock, would often have to step in and ask Paulson to "dial it down."
"It was not good because I'm not a singer, and it's just deeply nerdy," she says. "And Sandy would look at me and be like, 'Hey, dial it down, just stop.'"
The Emmy winner stresses that any impromptu song-and-dance routines were simply how she managed her "anxiety" while being around the R&B star.
"I dealt with my own anxiety by going up to Rihanna and being like, 'I've got a new song I can do for you,' and she's like, 'No, Paulson,'" she recalls to DeGeneres. "I'd be like, 'What about, I'm in a birdcage,' And she's like, 'No, you're not in a birdcage, and I really need you to stop singing.' She thought my lyrics weren't so bad, but my melody was terrible."
Paulson's on-set antics definitely weren't immune to the singer's famous "side eye."
"She gives great side eye," the actress says with a laugh. "The minute she does it, you're like, 'I'm really sorry.'"
Rihanna must not have been too turned off by Paulson's shenanigans, as the two briefly hung out at the recent Met Gala in New York City.
"We had a fun time watching Madonna at the Met Ball; she performed in this impromptu way. [Rihanna and I] are best friends," the actress jokes.
Paulson also elaborated on the "glamorous" custom-made Prada gown she wore to the grand fashion fete, noting that it took "800 hours for all that glorious beading" -- though she's not a big fan of red-carpet appearances.
"There's nothing worse than having all those cameras on you," she confesses.
Fittingly, Ocean's 8 follows eight cunning female thieves who attempt to take a pricey set of jewels from the annual New York City event. "Somebody is wearing a very, very fancy necklace to the Met Ball, and we are going to try to steal it," Paulson explains the plot to DeGeneres.
Watch below for more on the Ocean's Eleven spin-off, which hits theaters on June 8.