The resignation comes after Carey was criticised in a review of the church's handling of abuse carried out by Bishop Peter Ball, who was jailed in 2015 for historic offences against young men.
Rt. Rev. Dr. Steven Croft, the Bishop of Oxford, said he recently met the Carey regarding Dame Moira Gibb's review into the Peter Ball case which was released last Thursday.
He confirmed that Lord Carey has resigned from his role as honorary Assistant Bishop in the Diocese of Oxford.
Bishop Croft said: "Lord Carey has accepted the criticisms made of him in the Gibb review and has apologised to the victims of Peter Ball."
Lord Carey said in his statement on Thursday: "I accept the criticisms made of me. I apologise to the victims of Peter Ball.
"I believed Peter Ball's protestations and gave too little credence to the vulnerable young men and boys behind those allegations.
"I regret that after Peter Ball was cautioned I did not place his name on the Lambeth list."
He added: "Along with many others, I have been deeply distressed to read Dame Moira Gibb's report with its narrative of the abuse perpetrated by Peter Ball which remained hidden for so long.
"I hope that the focus of attention will continue to be on the survivors of abuse and offering to them the care and support they need."