His plea comes ahead of a vote on Wednesday by MPs over whether the Dubs Amendment scheme should remain open and a cap of 350 youngsters should be removed.
It was originally meant to take 3000 children but the government closed it prematurely, saying it was encouraging people traffickers.
Charities claimed the opposite and nearly 10,000 people signed a petition calling on the government to keep to Dubs scheme open.
Writing in The Times, Lord Rowan said: "Britain has a proud record of not standing by and leaving others to rescue the vulnerable.
"Along with tens of thousands of others today, I urge our parliament to make it plain that we treasure this national record and are ready to honour it once again."
Bishop of Chelmsford Most Rev Stephen Cottrell told Premier: "Christian people and other people of good will, people of other faiths, are coming together to say 'there are hundred and hundreds of children unaccompanied across Europe. They are a special case. We have in our a country a proud history of reaching out and excepting.'"
Lord Rowan continued: "It is precisely the lack of safe and legal routes, such as the Dubs amendment promised, which means that children will be more likely to put their lives in the hands of traffickers who wish to exploit them."