The petition was submitted in July but had not been made public.
Last November, the CIA concluded that bin Salman personally ordered the death of Khashoggi, despite the Saudi government's denials that the de facto ruler was involved.
In June, a United Nations investigator said in a report that there is credible evidence the crown prince bears responsibility for Khashoggi's death, though the Saudi foreign minister later called the report "flawed."
Although President Donald Trump had signaled that he would not take strong action against Saudi Arabia, a key US ally, or its crown prince, Secretary of State Mike Pompeo said earlier this year that Khashoggi's killers must "be held accountable."
The petition contends that the "Crown Prince's assassination of Mr. Khashoggi threatens international peace and stability" and "if left unpunished, the assassination will embolden Mohammed bin Salman to greater recklessness."