The petition has been gaining momentum online, amassing over 60,000 signatures in less than 48 hours.
"For decades Weird Al has entertained fans, young and old, with his popular clever parodies and unique sense of humor," petition organizer Ed Ball wrote on the website, "Having him headline the Super Bowl XLIX Halftime Show. [sic] would not only be overly accepted by the millions of views, but it would remain true to the standards and quality of the show business we have come to love and respect out of this prestigious event."
Ball said that performers previously parodied by Yankovic could join him during the hypothetical halftime set.
Yankovic himself has yet to comment publicly on the idea.
His most recent album, "Mandatory Fun," came in at No. 1 on the Billboard 200 chart when it was first released in July -- a career first for Yankovic after more than three decades in the industry.
Tell us: Do you want to see Yankovic at the halftime show?