Which game introduced the character Rosalina?

The game that introduced Rosalina was Super Mario Galaxy.

Released for the Wii in 2007, Super Mario Galaxy introduced Rosalina as a guardian of the cosmos and the caretaker of the star-like Lumas. She lives in the Comet Observatory, a starship that serves as Mario’s hub between the game’s many small planetoids and galaxies.

Rosalina’s role is more substantial than a brief cameo. Bowser steals the Power Stars that fuel the Comet Observatory, and Rosalina asks Mario to recover them. As players progress, they can read a storybook that reveals Rosalina’s childhood, her journey into space, and how she became the adoptive mother of the Lumas. This gave the character an unusually deep backstory for the Mario series.

Players sometimes confuse Rosalina’s debut with her later playable appearances. She became playable in games such as Mario Kart Wii and Super Mario 3D World, but those releases came after Super Mario Galaxy. She also appears in Super Mario Odyssey, including a small 8-bit appearance, but that game did not introduce her.