The Glasgow institution moved up three places in the QS World Rankings 2017 to join Juilliard in New York and The Royal College of Music in London.
Conservatoire principal Prof Jeffery Sharkey paid tribute to a "great team working in a great city and nation" who delivered "innovative" arts education.
Established in 1847, it has about 1,100 students from 52 countries.
It offers courses in music, dance, drama, film and production.
Famous alumni include David Tennant, James McAvoy, Alan Cumming, Ruby Wax, Katie Leung, Melody Grove, Colin Morgan, Richard Madden, Sir David McVicar, Patrick Doyle and Elaine C Smith.
Conservatoire chairman Prof Nick Kuenssberg said The Royal Conservatoire of Scotland was "a place like no other".
He said: "Principal Jeffrey Sharkey and our team already lead the way in higher education in Scotland for the employability of graduates and their commitment to widening access.
"I'm thrilled to see their dedication and innovation rightly recognised as global leaders in the field of performing arts education."
The world ranking comes a few weeks after the conservatoire celebrated the completion of its Â£2m Creative Campus, which has increased learning and teaching space by 50%.
The Royal Conservatoire of Scotland has been ranked in the world top three for performing arts education.