Ture, formerly known as Stokely Carmichael, is visiting South Africa for a few weeks and will participate in national events to honour Biko, who was killed in September 1977 while in police custody.
"It (the application) is not a bad step, but I believe that when one commits a crime one should make amends for what one has done," Ture said at a media briefing organised by the Azanian People's Organisation at a Johannesburg hotel.
Azapo deputy president Pandelani Nefolovhodwe said Ture had contributed to the liberation struggle in South Africa.
"Comrade Ture, like our own Steve Biko, is a well-known firebrand of black consciousness, whom many among us drew inspiration from from his speeches," Nefolovhodwe said.
"Ture is the one who influenced events in Africa and around the world," he said. Ture is an American who has been a resident of Guinea for over 25 years.
The Biko memorial committee said a return train trip from Pietersburg to King William's Town had been organised for supporters who wanted to attend the unveiling of Biko's tombstone at his home in Ginsberg on Friday.
The train would leave Pietersburg on Thursday morning, pass Johannesburg on Thursday afternoon and reach King William's Town on Friday morning. The trip would cost R120.
Anyone who needed information on the train trip should contact Azapo national organiser Strike Thokoane on (011) 988-1255.