The actor can be heard on the track London Boy, which Taylor is believed to have written about British boyfriend Joe Alwyn.
Idris, who co-stars in the upcoming film adaptation of Cats alongside Taylor, features at the very start of the song, and is heard saying: “We can go driving on my scooter.”
The pair’s co-star James Corden is also featured, and can be heard simply shouting: “Oh!”
On the track, Taylor alludes to The Favourite star Joe, as she sings about ‘walking through Soho/ Drinking in the afternoon’ and ‘Watching rugby / With his school friends.’
Taylor and Joe are thought to have been dating since 2016, after her romance with another British star, Tom Hiddleston, ended.
Her new album – her seventh in total – is the follow up to 2017’s Reputation, and includes the singles Me!, You Need To Calm Down and Lover.
She described it as “celebration of love, in all its complexity, coziness, and chaos”.
In a tweet marking its release, Taylor referenced her on-going row with Scooter Braun, after her back catalogue was bought by the talent manager.
She said it was “the first album of mine that I’ve ever owned”.
Taylor had been singed to Big Machine since her music career started as a teen, and the label owned the rights to her first six albums, including 2008’s Fearless and 2014’s 1989.
In June, Scooter Braun’s company Ithaca Holdings announced that it had acquired Big Machine Records in a deal believed to be worth around £237 million, meaning he owned the master recordings of all of Taylor’s previous releases.
Taylor signed with Universal Music Group in November last year, in a deal ensuring she maintained the rights to her work.
The singer and Scooter have become involved in a public row after she alleged she’d not been told about the deal before the news was made public, accusing Scooter of “incessant, manipulative bullying”.
She has since announced plans to re-record her previous albums.