In a statement Wednesday, the rock band said they have not given permission to the Trump campaign to use their songs and "have requested that they cease all use immediately."
A Trump campaign spokeswoman didn't immediately respond to a request for comment or say whether they had a license to play their songs.
Trump, an avid music fan, has featured Rolling Stones songs at his rallies for months as part of a diverse soundtrack that includes Elton John, opera and classic rock songs. The Rolling Stones' 1969 classic "You Can't Always Get What You Want" was a popular song for his events, and during an event on Tuesday night, the campaign played "Start Me Up."
Adele and Aerosmith frontman Steven Tyler both asked the candidate to stop using their recorded songs to fire up crowds. Neil Young also objected when the real estate mogul used "Rockin' in the Free World" during his campaign kickoff announcement last year. In those cases, the Trump campaign stopped using the songs.
Political campaigns don't need artists' permission to play their songs at rallies as long as the political organization or the venue has gotten what's known as a blanket license from the performing rights organizations ASCAP and BMI for all the music in the licensing group's repertoire.
But artists do have some recourse. BMI, for example, has said it has a provision in its license agreement that allows BMI songwriters or publishers to object to the use of their songs and they have the ability to exclude those songs from the blanket license.