"When I grow up, I will..." is most common, we often ask kids 'what do you want to be when you grow up?' and this is how they answer.
"When I'm grown up, I will..." sounds a bit more childish but it's fine
"When I have grown up, I will [have]..." is odd to me. I think it's a different tense structure. e.g. "When I've studied languages before, I've used italki" is fine -it implies something you've done multiple times.
Sidenote: there's a great song called 'When I grow up' from the musical Matilda - it's on youtube if you want to watch it!