"I Call Your Name" was mostly written by John Lennon, although it was credited to the team of Lennon/McCartney. According to journalist David Sheff from his interview with Lennon, Lennon wrote this song before the formation of the Beatles.
Lennon originally turned the song over to The Dakotas, another Liverpool act, at the time when George Martin was also working with them. Lennon wasn't happy with The Dakotas arrangement of the song and its poor B-side performance, so he had The Beatles re-do it
, releasing it for the first time in the US on The Beatles' Second Album
This cover by The Mamas & The Papas seems as if they were trying to compensate Lennon for his disappointment with The Dakotas version. That sunny honky-tonk piano with their trademark full-rounded vocals and the well-realized instrumental bridge certainly grabs your attention.