Affleck's short film, 'Gimme Shelter', is set to the Rolling Stones' song of the same name, which the band has donated to the campaign.
The video footage was shot last month in the Democratic Republic of the Congo's (DRC) strife-torn North Kivu province, where some 250,000 civilians have fled for their lives since fighting resumed in August between government forces and rebel troops.
Affleck said: "We made this film in order to focus attention on the humanitarian crisis in the DRC at a time when too much of the world is indifferent or looking the other way.
"The suffering and loss we've all seen first-hand is staggering -- it is beyond belief.
"I'm urging people not to look the other way, not to turn off their TV when news of the violence in the DRC comes on.
"We all need to stand up and support the work of organizations like UNHCR who are on the ground offering protection and working hard to ensure the rights and well-being of refugees."
'Gimme Shelter' captures the suffering of internally displaced Congolese families who fled the fighting with next to nothing and are now forced to find refuge in makeshift shelters with little to live on.
The film will be distributed worldwide via the internet, television, mobile phones, cinemas and hotel chains to raise awareness of UNHCR's global work for refugees and to encourage donations for displaced Congolese.
UNHCR is hoping to raise $23m from the campaign to pay for clean water supplies and emergency humanitarian assistance kits that contain jerry cans, kitchen sets, thermal blankets, sleeping mats, mosquito nets and plastic sheeting needed for construction of shelters.
The UN refugee agency said there are currently 1.3m displaced people in the DRC, many of them earlier victims caught up in a continuing cycle of violence.
The effects of the conflict have reportedly claimed as many as 5.4m lives in the last 10 years, with an estimated 1,000 people still dying every day.
Jagger expressed strong support for the campaign: "The Rolling Stones are very happy to contribute 'Gimme Shelter' in support of Ben's efforts to raise the profile of the conflict in the Congo. I hope this video will help."
Affleck, who has starred in films 'Good Will Hunting' and 'Pearl Harbour' and gained plaudits for directing 'Gone Baby Gone', has made four visits to central Africa since 2007.
UN High Commissioner for Refugees Antonio Guterres said: "Refugees are among the most vulnerable of the vulnerable and we at UNHCR are grateful for the compassion, concern and commitment shown by those involved in this campaign.
"Their contributions will have a direct impact on the lives of uprooted people not only in the DRC, but around the world."