Yes, in fact, Sarah has said nothing like what the birthers who posted this alleged.
So once again, it's just more birther BS.
https://en.wikipedia.org/wiki/Barack_Obama_citizenship_conspiracy_theories
Sarah Palin
During a December 3, 2009 interview on Rusty Humphries’ radio talk show, Humphries asked Sarah Palin if she would make Barack Obama’s birth certificate a campaign issue in 2012, should she decide to run. Palin responded, “I think the public rightfully is still making it an issue. I don’t have a problem with that. I don’t know if I would have to bother to make it an issue, because I think that members of the electorate still want answers.” Humphries followed up, asking whether she thinks Obama’s birth certificate is a fair question to be looking at. Palin answered, “I think it’s a fair question, just like I think past association and past voting records – all of that is fair game. The McCain–Palin campaign didn’t do a good enough job in that area.”[125]
After news organizations and blogs picked up the quotation,[126] Palin issued a statement on her Facebook page in which she clarified that she meant to say that voters have the right to ask questions, and she herself has never asked Obama to produce a birth certificate. She then went on to compare questioning of Obama’s birth certificate to questions that were raised during the 2008 presidential elections about her maternity to her son, Trig.[127] This analogy was criticized by Mark Milian of the Los Angeles Times, who commented that “It’s not like Barack Obama hosted a radio show and called her a baby faker.”[128] In addition, Andrew Sullivan, an established skeptic of Palin’s relationship with Trig, wrote in response to her comments: “Palin has never produced Trig’s birth certificate or a single piece of objective medical evidence that proves he is indeed her biological son.”[129]