Dr Rowan Williams has also spoken out about "unfounded" claims that the UK is "full".
Speaking ahead of Refugee Week, which begins on Monday, he told the BBC the UK could not ignore the refugee "crisis".
The Government has agreed to resettle 20,000 Syrian refugees by the year 2020.
So far around 1,600 have already arrived in the country.
Dr Williams, chairperson of Christian Aid, said the crisis is the largest displacement of people since the Second World War.
He said: "Desperate people who have been driven out of their homes by war are being forced to make dangerous journeys in search of sanctuary.
"Yet many countries are closing their borders and putting up barbed wire."
He went on: "The UK must not turn a blind eye to this crisis.
"We can and must do more to respond."
A Syrian refugee woman tries to clean the mud from her clothes in an improvised camp on the border line between Macedonia and Serbia, near northern Macedonian.
The archbishop has followed in the footsteps of many Christian leaders who have urged leaders to welcome their neighbours.
Dr Rowan Williams spoke about Britain's long history of providing sanctuary to refugees, from children escaping Nazi Germany to Kosovans caught up in the Yugoslav wars of the 1990s.
He also praised the role refugees have played in British society, saying: "The rhetoric in the media is one that suggests that the UK is 'full', and that those arriving on our shores are a drain on our economy.
"Not only are these assertions unfounded, but they fail to recognise the positive, life-affirming contributions that generations of refugees have made to British society - and that we ourselves are changed by welcoming the stranger."
Refugee Weeks begins on Monday and Christian charity World Vision estimates there are around 62 million refugees around the world at this present time.
