What figure of speech is "this is not my first rodeo"?
This phrase is an example of an idiom. An idiom is a culturally-based expression. Often idioms are used by enough people that most others will understand will they say. Idioms also inject humor into speech.
Idioms often possess a meaning other than their grammatical or logical ones and cannot be directly translated into another language. (enotes)
This idiom is a type of metaphor. The person speaking is using figurative language. The person has mostly likely not actually been in a rodeo. Instead, he is trying to tell whoever he is talking to that he knows what he is doing. Another idiom like this is “I was not born yesterday.” In both cases, the expressions can be used as angry or humorous retorts. The phrase seems to have originated from a country music song by Vern Gosdin