"Time Warp" was the fifth song in the original stage show (after "Science Fiction/Double Feature", "Dammit Janet", "Over at the Frankenstein Place" and "Sweet Transvestite") where it was performed by Riff-Raff (Richard O'Brien), Magenta (Patricia Quinn), Columbia (Nell Campbell) and the Narrator (Jonathan Adams), but fourth in the film (following "Over at the Frankenstein Place" and preceding "Sweet Transvestite"). O'Brien, Quinn and Campbell reprised their roles from the stage production in the film but the Narrator, now renamed the Criminologist, was instead played by Charles Gray. In the 2016 TV production, The Rocky Horror Picture Show: Let's Do the Time-Warp Again, the number was performed by Reeve Carney (Riff-Raff), Christina Milian (Magenta), Annaleigh Ashford (Columbia) and Tim Curry (the Criminologist).
Stage productions continued to use the original placement until Richard O'Brien revised the script for the 1990 West End revival in which he moved the song to the film's placement. For reasons of pacing, most productions now follow this order.