Passive by Perfect Circle was a song on the soundtrack of Constantine. Here is a fan made video featuring the movie and the song.
Another fan did Call Me by Shinedown but personally we would like to see one to the above's Ozzy's Hellraiser. Constantine was the star of the Hellblazer comic which was originally intended to be called Hellraiser, but this title was revised before publication due to the contemporaneous release of Clive Barker's unrelated film of the same name.
Here is a deleted scene where they tried to Exercise Constantine.
In our podcast we also mention that Constantine's look was based on Sting from the police