The song is actually called Cry, not The Cry. It has always been a short introduction to The Electric Co. when it is played live.
It was first released on the 1981 single Fire on the second disc of the special 2 disc 7 inch single. The normal Fire single has J. Swallo as the b side but some singles had a second live disc and this is where Cry was first released. This version is from the March 6, 1981 Boston concert and on the label of the single (which I own) the song is clearly labelled Cry, instead of The Cry.
The song was later released on Under A Blood Red Sky, but is not listed anywhere on the cover or label. This is where most U2 fans own the song and as it is not listed, most fans do not realize that it is its own song and not actually part of The Electric Co.
The guitar riff from the song was later used for the October song Is That All?
The version Bono is singing on the Vertigo tour features completely different lyrics than on the 1980s versions.