"Yung Rapunxel" was originally set to be released on March 26, 2013. However, on March 28, 2013, it was announced that the single would drop on April 16, 2013. The first single from Broke With Expensive Taste was initially planned to be "Miss Amor/Miss Camaraderie". Nevertheless, on January 28, 2013, Banks acknowledged that the first single was going to be "Yung Rapunxel". The original release date, which was the February 12, was delayed to March, and then again, delayed to April 16, 2013. For unknown reasons, it is now unavailable on iTunes UK. On March 9, the artwork for the single was released via Banks' Twitter account.
Michael Depland from MTV Buzzworthy described "Yung Rapunxel" as a 1990s Hi-NRG-influenced hip house song, which is built on a busy witch hop beat. Meanwhile, The Guardian's Alex Macpherson detailed the track as an industrial number.
Spin's Marc Hogan wrote that the song "comes across as a reinvention for her, though it doesn't have quite that track's instantly memorable catchphrases... Finally, Banks has left seapunk behind to go where she belonged all along: another galaxy". MTV's Michael Depland believed that on the track, "A bona fide hip-house banger, Azealia rhymes slickly (and NSFW-ly) over a busy witch-hop beat", that Banks is "back spitting fire over a manic '90s HI-NRG-influenced track, which is cut in between muffled hollers".
Shooting for the music video began on February 22, 2013, and was continued into March. The official music video was released on April 16, 2013. The video was created by visual artist Jam Sutton. The video features a mostly black-and-white setting, including police running through mist, owls with yellow and red eyes flying in suspended motion, Banks riding a mechanical bull, a rotating Yin & Yang symbol, a disembodied hand with an eye embedded in the palm floating in mid air and Banks with mouths for eyes.