The 29-year-old was jailed for six years last March for sexually touching and grooming the 15-year-old fan.
He was refused leave to appeal his conviction and sentence in July, but launched a second bid late last year.
A panel of three appeal judges turned down the former Sunderland player's latest bid.
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Mr Kenyatta beat Mr Odinga comfortably by 50.07% to 43.28% on 4 March, avoiding a run-off by only 8,100 votes.
But Mr Odinga has accused the electoral authorities of manipulating the result.
Police fired tear gas to disperse about 100 supporters of his Coalition for Reforms and Democracy (Cord) who had gathered outside the Supreme Court.
The police had warned them that they would not be allowed to do so.
Some of the crowd were wearing t-shirts bearing slogans including "I support the petition" and "Democracy on trial".
The presidential, legislative and municipal elections held 12 days ago were the first since the 2007 poll which set off ethnic and political violence in which more than 1,200 people were killed.
Mr Kenyatta and his running mate, William Ruto, are facing trial on charges of crimes against humanity at the International Criminal Court (ICC) for allegedly fuelling the unrest. They deny the charges.
Lawyers for Mr Odinga said their petition to the Supreme Court included allegations of vote manipulation, as well as problems with the registration of voters and an electronic vote counting mechanism.
"I have no hesitation whatsoever in lawfully challenging the election outcome," Mr Odinga told reporters outside his offices in Nairobi.
"These failures dwarf anything Kenyans have ever witnessed in any previous election," he added.
However, the prime minister urged his supporters not to resort to violence.
"We cannot begin what is supposed to be a new era under a new constitution in the same old ways," he added, referring to the charter adopted in 2010.
The Minister of Lands, James Orengo, a senior Cord official, said the party had a constitutional right to file the petition and a "strong case".
"Expect a new election, and this time around no monkey-business. I think we're going to win and win in the first round," he told KTN TV.
"I can assure you that we have the evidence, and we have the will and the preparedness to prosecute the petition," he added.
Mr Orengo nevertheless promised that Cord would respect the Supreme Court's ruling if it went against the party, and urged Mr Kenyatta and his supporters to declare that they would do likewise.
In his acceptance speech last Saturday, Mr Kenyatta described the election as "free and fair" and a "triumph of democracy".
The Independent Electoral and Boundaries Commission (IEBC) has also insisted that the vote was credible and that it is ready for any legal scrutiny.
International observers said the election was largely free, fair and credible, and that the electoral commission had conducted its business in an open and transparent manner.
Mr Odinga was the runner-up to Mwai Kibaki in the 2007 presidential election, which he also said was stolen.
Ex-England footballer Adam Johnson has lost a Court of Appeal challenge against his conviction for sexual activity with a schoolgirl.
[NEXT_CONCEPT]
Kenyan Prime Minister Raila Odinga has filed a Supreme Court appeal against Uhuru Kenyatta's narrow victory in the presidential election's first round.