On Monday he lodged a first incident report at an Islamabad police station against Rizzo, accusing him of six murders as well as conspiracy to kill a large number of Pakistani citizens.
In an interview with Newsweek earlier this year, Mr Rizzo, 63, admitted approving drone targets.
"How many law professors have signed off on a death warrant?" he said.
The case put together by Mr Akbar centres on three strikes.
The first, in North Waziristan, hit a house during Ramadan, killing three relatives of a 15-year-old boy, who also lost his legs.
The second case is brought by Kareem Khan, a journalist whose brother and son were killed by a drone in 2009. Last year he lodged a murder case against Jonathan Banks, the then CIA station chief in Islamabad who had to be whisked out of the country.
And the third complaint is brought by Maezol Khan, whose son had been sleeping outside when he was killed by shrapnel from a drone strike South Waziristan, also in 2009.
Mr Akbar said his team was piecing together evidence from other strikes and would use it to launch proceedings in the US and UK against anyone involved in flying drones, supplying intelligence or approving their use.
"It will be like the Nuremburg trials. If you follow an illegal order you should be held to account. If you kill an innocent person, that's murder," he said.
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