James Gunn has promised that we will learn more about Rocket in upcoming Marvel Studios projects:
"As you know, the MCU is one way of processing these characters. 616 is a different one. We are going to learn more about where Rocket comes from in the coming sagas. It's going to be a little different from the comics. We already know a lot about from where he came from. It's a little bit more horrible than what it is in the comics when you come down to it. We will learn more about that."
In Guardians of the Galaxy, Rocket self-identifies as an individual who has been "torn apart and put back together over and over and turned into some little monster" - and surely that's a significant part of what James Gunn is referring to when he notes that the backstory is a bit more "horrible" than the comics. It seems that the diminutive Guardian began his life as an ordinary raccoon (a species that Peter Quill, Drax and Nebula could all identify), was abducted by scientists, and was transformed into the anthropomorphized being we know and love. While he goes by Rocket, he's officially identified as Subject: 89P13, and is described as a "cybernetic/genetic experiment on a lower life form" on his rap sheet. This is all we know, however, and there surely is a lot more that can be revealed as part of an attempt to flesh out the character's history.