Perry extended the offer on her Twitter account and shared a picture of the two together at a recent meeting.
“I told @hillaryclinton that I would write her a ‘theme’ song if she needs it,” Perry wrote.
Clinton — who has not yet officially declared her candidacy for 2016 — responded with a message praising Perry’s music June 22.
The politician has been on the press circuit in promotion of her new book Hard Choices.
Perry recently launched her own record label.