The Complaints Response Unit (CRU), launched last Friday, is the first in the country's history and aims to use "cutting edge technology to combat crime and address complaints of citizens".
"CRU will deal with complaints against police professional misconduct," national police spokesman Abayomi Sogunle said.
"It will open up a channel of communication between the police and the Nigerian community," he told Nigeria Info radio.
Disgruntled members of the public can phone in their complaints or send them via email, social media platforms Twitter, Facebook or WhatsApp directly to the inspector general of police's inbox.
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Nigeria's police are frequently criticised for being impolite, ill-trained and poorly-equipped. They have also been accused of bribe-taking and human rights abuses.
A September 2014 report by Amnesty International said torture had become so commonplace in Nigeria's criminal justice system that some police stations even have an officer in charge of the practice.
President Muhammadu Buhari has embarked on a wide-ranging anti-corruption campaign and an overhaul of the police service is expected.
The scheme's objectives will be translated into local languages for as wide a reach as possible, he added.