The chocolate manufacturer has already changed its Dairy Milk bars and bags of chocolate Buttons to Fairtrade.
Now the development agency wants to see the same thing happen with Twirls, one of Cadbury's most popular chocolate bars.
The FairTwirl Campaign is asking Cadbury to commit to a date by which Twirl chocolate bars will be Fairtrade.
Fairtrade addresses injustices in pricing and working conditions, and seeks in particular to ensure that farmers and producers are not exploited.
The campaign asks supporters to sign the Fair Twirl petition and post the petition on their Facebook walls or Twitter feeds.
It is part of Tearfund's Emerging Influencers programme and is being supported by MPs Frank Dobson and Martin Horwood.