Rt Revd Paul Butler has said the newspaper's support of taking in the children despite being "trenchant supporters of very restrictive immigration rules" shows the government was wrong to oppose the measure earlier this week.
The government narrowly defeated the motion to take in 3000 lone Syrian children in Europe in the House of Commons on Monday, with 292 MPs voting against the proposal and 272 in favour.
The Daily Mail is traditionally known as a conservative paper which is supportive of restricted immigration policies.
In an editorial piece called 'The Mail's always been robust on migration. But we MUST give these lost children sanctuary', it said: "We believe that the plight of these unaccompanied children now in Europe - hundreds of them on our very doorstep in the Channel ports of France - has become so harrowing that we simply cannot turn our backs.
"It is not their fault, after all, that they've been sent halfway round the world alone to search for a better life, often after seeing family members slaughtered.
"Every instinct of our hearts must surely be to play our part, looking after at least some of these neglected children until, God willing, conditions become safe enough to return them to their families in their homelands."
Some Twitter users were surprised at the Daily Mail's piece:
You know the Tory government is being too harsh when even the Daily Mail says we should accept the refugee children— Stuart Gray (@randomelginguy) April 28, 2016
Rt Revd Paul Butler said: "I welcome the Daily Mail's call today for unaccompanied child refugees to be offered asylum.
"Unless they are offered help and hope, children at risk will fall victim to trafficking and all kinds of evil.
"As a nation we must show kindness and compassion to children at risk, playing our part in offering proper refuge to those already in Europe whose lives are deeply traumatised.
"There is now a broad coalition for action, and the House of Lords latest amendment offers a clear way forward for the Government.
"When even trenchant supporters of very restrictive immigration rules call on them to accept this amendment, I hope the Government will recognise that it is time for them to agree to this proposal."