There is official cardboard app for iOS: https://itunes.apple.com/gb/app/google-cardboard/id987962261?mt=8
Cardboard puts virtual reality on your iPhone. The Google Cardboard app helps you set up a Cardboard viewer and includes a few experiences to get you started
(but doesn't allow to watch existing YouTube videos)
There is support page for 360 degrees videos: https://support.google.com/youtube/answer/6239930?hl=en-GB
With Cardboard and the YouTube Android app, you can even watch 360 degree videos for an immersive experience
(emphasis mine - feature is supported in Android - not iOS)
EDIT: I did some more research
Then type #360video into YouTube, look for the VR icon and strap on a viewer to see 2D online vids via your headset.
(confirming with the author)
Is there an app (either paid or free) that allows to display video in cardboard format on iOS devices?