After looking into TyrionLannister's answer, I found this on wikipedia:

Bugs Bunny's nonchalant carrot-chewing standing position, as explained by Chuck Jones, Friz Freleng, and Bob Clampett, originated in a scene in the film It Happened One Night, in which Clark Gable's character leans against a fence, eating carrots rapidly and talking with his mouth full to Claudette Colbert's character. This scene was well known while the film was popular, and viewers at the time likely recognized Bugs Bunny's behavior as satire.

And this

After looking into it, I found this on wikipedia:

Bugs Bunny's nonchalant carrot-chewing standing position, as explained by Chuck Jones, Friz Freleng, and Bob Clampett, originated in a scene in the film It Happened One Night, in which Clark Gable's character leans against a fence, eating carrots rapidly and talking with his mouth full to Claudette Colbert's character. This scene was well known while the film was popular, and viewers at the time likely recognized Bugs Bunny's behavior as satire.

And this