The 16-year-old was gang-raped and then thrown in a pit latrine breaking her back.
The three men accused of gang-raping her were ordered by police to cut grass as punishment.
The petition signed by 1.2 million people calls for the immediate arrest and prosecution of the alleged rapists.
The BBC's Anne Soy said about 300 people walked from Uhuru Park in the capital, Nairobi, to the police headquarters to hand over the petition, which was carried in cardboard boxes.
David Kimaiyo, the inspector general of police, was not present to receive it, but sent a representative on his behalf, she says.
The girl, referred to as Liz to protect her identity, was attacked and repeatedly raped after returning from a grandfather's funeral in a village in Busia in western Kenya.
Her unconscious body was thrown into a pit latrine and she is now in a wheelchair.
When she was rescued she said she had been attacked by a gang of six men, but she could only identify three of them.
They were then detained by villagers and taken to the police, who chose not to officially prosecute them. Instead they ordered them to cut grass around a police station in Busia, near Lake Victoria.
This spurred some journalists and activists to use social media to raise awareness of the case, using the hashtag #Justice4Liz.
An online petition was then set up by activist Nebila Abdulmelik on the Avaaz petition hosting website, which started to gain international attention.
"It's incredible that more one million people have backed the campaign calling for action on the rape of Liz," she said in statement released by Avaaz.
"Rather than deleting tweets, Inspector Kimaiyo has to take action in what has been a shameful response by Kenya's police.
"The men that raped Liz must be arrested and the police officers who let them walk free must be held to account - this case has to be the moment when the culture of violence and impunity ends."
We need to pray that this will be the case - the end of the culture of violence and impunity. It won't start until police take cases like this seriously. The police involved must be made examples of.
Our reporter says the protesters carried placards - some reading "Justice for Liz" and "One in three of us will be violated in our lifetime" - which they left outside the police headquarters.