The 1982 Film
When we first meet Rooster and Lily, they are in Miss Hannigan's office and that he was supposed to be in jail, but they let him out early (good behaviour) and while Miss Hannigan is distracted, he steals money from her purse.
When Annie escapes with Mr Warbucks check and tears it up, he immediately chases after Annie indicating that he was gonna kill her. But is delayed by his sister, whom he knocks out.
The 1999 Version
He is first seen having escaped from jail after conning the Warden into letting him out early. That's when he shows Lily to his sister. He knew an artist in Brooklyn making fake birth certificates and all those cons didn't have a sister who knew everything there was to know about Annie.
Near the end of the 1999 film, his real name is exposed as Daniel Francis Hannigan.
Because he had been arrested in the 1982 film, he is not seen (or even spoken of) in Annie: A Royal Adventure!.
Rooster is played by Tim Curry in the 1982 film and Alan Cumming in the 1999 film.