Subject-verb inversion is often done for emphasis. https://www.ecenglish.com/en/social/blog/san-francisco/2011/11/28/grammar-lesson-inversion-and-emphasis

"Have you got news for me?" "Have I got news for you?" Answering a question with a question this way is a way of saying "Yes", but in a more dramatic way. I would definitely think this person has news for me, and it sounds exciting. For some reason I think it might be a cultural language device originating from New York. The title of the show presupposes the initial question, although the device seems to have evolved to a statement in itself without the need for a leading question. "I have got news for you" is still a grammatically correct statement though.

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