Jesus College said it was taking down the statue known as "Okukor" from the former kingdom of Benin, which is now part of southern Nigeria, and was looking at the possibility of its repatriation.
"Jesus College acknowledges the contribution made by students in raising the important but complex question of the rightful location of its Benin bronze, in response to which it has permanently removed the Okukor," a college spokeswoman said.
Last month, Jesus College's student union passed a motion that said the statue was looted by British troops in 1897 during a "punitive expedition".
The students' "Benin Bronze Appreciation Committee" said it was in contact with a Nigerian government minister who supported its repatriation, according to minutes of the meeting on the union website.
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"Considering the moral case and the positive benefits outlined in the proposal the time is now right to repatriate the cockerel to the Royal Palace of Benin in line with existing protocol," the motion said.
The college said it would remove a plaque honouring Rhodes, a white supremacist like many builders of the British empire, but would keep the statue in place.
The campaign has since widened to target other figures associated with British colonial history, including queen Victoria.