The petition followed reports that Oprah decided not to involve her TV show in the presidential campaign. Earlier this year, Oprah endorsed Barack Obama in his run for the Oval Office.
In a statement to the Drudge Report last week, Oprah's show said she would love to interview Ms. Palin, the governor of Alaska, and predicted it would be a "fantastic interview" but said it could only take place after the election.
"At the beginning of this presidential campaign when I decided that I was going to take my first public stance in support of a candidate, I made the decision not to use my show as a platform for any of the candidates," the statement quoted by the Drudge Report said. In the past, Oprah has interviewed presidential candidates.
The GOP petition urges Oprah to change her mind.
"Oprah Winfrey is an inspirational figure to millions of Americans, who admire her strength, resilience, and force of character. She has become a role model, and an example of someone who overcame hardship and stereotypes to build the life she wanted.
"That is why we respectfully ask that Oprah reconsider her position concerning a public interview with the Vice Presidential candidate Sarah Palin. Like Oprah, Ms. Palin has carved out her own path in life, from pursuing a career in a field (and political party) dominated by men, to her difficult choice to raise a child with Down Syndrome.
An official of the Oprah program did not immediately return a call for comment.