Most of Haiti's debt is owed to the International Monetary Fund and the Inter-American Development Bank, as well as other creditors, including Taiwan and Venezuela.
The UK cancelled its bilateral loans to Haiti last year. Christian Aid now wants the Chancellor to use his influence with the creditors to see the devastated country's remaining debt cancelled.
The petition calls on Mr Darling to ensure that all money given to Haiti for emergency relief and development in the future is in the form of grants and not loans.
"Christian Aid is responding to the disaster in Haiti with emergency aid. But we need to help Haiti in the long-term as well as the short-term," the petition reads.
"We are now calling on the UK to lead the world in giving Haiti a fighting chance for the future by cancelling its $890m of international debt."
Christian Aid has dispatched £250,000 for emergency relief to survivors of last week's massive earthquake, which it plans to distribute among some 15,000 people.
"We are hoping for a huge response, which will symbolise the UK public's overwhelming desire to see our government help Haiti at its time of crisis," said Paul Brannen, head of Advocacy and Influence at Christian Aid.
"When 200,000 people are feared dead and countless more have had their bodies and their lives shattered by horrific destruction which will take years to repair, how can lenders still be demanding their money back?"
He continued: "We know that people in the UK care deeply about the horror and devastation which have engulfed Haiti, because they have given so generously to the DEC Appeal for the country.
"This petition is a further opportunity for the public to support the people of Haiti, by adding their voices to the call for the country's massive debt to be cancelled now."
Christian Aid will present the petition to the Chancellor at the end of the month.
Survivors are still being pulled from the wrecked buildings in capital Port-au-Prince more than one week after the 7.0 magnitude quake struck.
A 69-year-old woman rescued after being trapped in the rubble of a cathedral for one week said her Roman Catholic faith had kept her going.
Ena Zizi, who suffered a dislocated hip and broken leg, said she talked "only to my boss – God – and I didn't need any more humans", according to the Daily Record.
In another miracle survival, French radio said a 23-day-old baby had been rescued from the debris of a flattened house in Jacmel, southern Haiti, on Wednesday.
Haitian government officials told the European Commission as many as 200,000 people may have died in the quake, while an estimated two million people have been left homeless.
The US is to send another 4,000 troops to Haiti to help distribute food and medical supplies across the country. It raises the number of US troops there to 16,000.
As the scale of the devastation continues to unfold, the Disasters Emergency Committee, a group of the UK's 15 leading aid agencies, said donations to its appeal have reached £31.5 million.
The Christian Aid petition can be signed at act.christianaid.org.uk/ea-campaign