The charity is also tackling the environmental threat posed by the UK's 'disposable society' by teaming up with recycling firm Office Green Technologies (OGT).
Phones can be donated to the trust via freepost and each one recycled could be worth up to £65 for the charity, which hopes to raise £20,000 in the next year.
National Trust spokesperson Kristy Jones said the drive would initially target visitors to trust properties, as well as its members and volunteers.
The campaign would then be stepped up around Christmas when many people upgrade their phones.
The charity also hopes to persuade mobile phone firms to promote the campaign.