On 12 August 2009, the song was leaked via BitTorrent. A text file accompanying the leaked track contained a cryptic poem and reference to a release date of 17 August. On that date, guitarist Jonny Greenwood posted a note on the band's blog Dead Air Space announcing that "These Are My Twisted Words" was available free from the website as a standalone download or a torrent hosted by Mininova free of charge. The download came with various artwork pictures by Stanley Donwood and Thom Yorke to be printed on tracing paper and put "in an order that pleases you." Some have speculated that the band leaked the song themselves following the unconventional self-release of their album In Rainbows (2007).
The song was noted for its unorthodox release. Ryan Dombal of Pitchfork Media described the song as "very Radiohead-y", while pointing out that the track's "nauseous guitars, featherweight motorik beat, and vaguely whiny lyrics almost read as parody". He concluded that the song "isn't as enciting as its method of distribution". Brian Parks of PopMatters gave the song a positive review, writing that "the five-and-a-half-minute track opens with three minutes of ominous instrumental krautrock and is the most recent in a long line of unconventionally beautiful songs for which Radiohead is renowned". Daniel Kreps of Rolling Stone also noted the krautrock influence, also pointing out Thom Yorke's trademark croon and the similarities between the song and In Rainbows track "Weird Fishes/Arpeggi." Matthew Schnipper of The Fader commented that the song is "a simple song" and "a straightforward declaration of no weirdness, backed by the horse hoof snare and light cymbals of drummer Phil Selway."