The song, which riffs on The Sound of Music's My Favourite Things, was played 16.9m times last week, a chart record.
Mariah Carey's All I Want for Christmas is You was the previous record-holder, with 15.3m plays in a week last month.
7 Rings is also the first single to sell more than 100,000 copies since the Grenfell charity single in June 2017.
Grande's song is a tongue-in-cheek hymn to retail therapy, inspired by a trip to Tiffany's last year, where she bought her friends matching diamond rings.
It came with a lavish video, set in a neon-lit house, where the champagne is flowing and the props are almost entirely pink.
On YouTube, the video was watched 23.6 million times in its first 24 hours and has now been played more than 72 million times.