I heard both versions of this sentence and I wonder which one is the correct one. In the Google translator it says "Io faccio", but in the real world I heard multiple times "Faccio io".
Both are short sentences consisting of two words: Io is “I”, the first-person pronoun; faccio is the first person of the present tense of the verb fare, “to do”.
This said, both are possible Italian sentences, with different meanings. Io faccio simply, plainly means “I do” and lacks an object. The person you are speaking to would likely ask you something like Fai che cosa? (“You do what?”).
Faccio io is used only in specific contexts, since it stresses the io part, almost as in: “Step aside and let me do it”.