A music video to accompany the release of "Baby Come Home" was directed by Lorenzo Fonda (the video was shot at the end of March in Hollywood studios) and first released onto YouTube on May 30, 2012 at a total length of three minutes and fourteen seconds. The video shows the band members dress up as a variety of characters. Jake Shears can be seen as a nun and knight in scenes, while Ana Matronic becomes a sailor and a witch.
Lewis Corner of Digital Spy gave the song a positive review stating:
As such, we breathed a sigh of relief when the four-piece confirmed 'Baby Come Home' as their next single. Partly because its mix of bouncy piano and funky guitar is more addictive than a game of Temple Run, but mainly because it recalls classic Scissor Sisters circa 2004. It's a welcome reminder of their roots and one that deserves to replicate some of their heyday success. .