The system uses satellite positioning, navigation and timing technology, which is able to pick up natural objects such as trees.
If the scheme proves successful it could be expanded further so that members of the public can use it on smartphones or mobile devices.
Working with Bartec Auto ID - the same company who developed in-cab technology in the City Council's refuse and recycling vehicles - officers are trialling five hand-held devices that can identify the precise location of a tree and input relevant information onto the system.
Currently tree officers have to use traditional mapping to pinpoint a tree and the information is fed into an iPad whilst on location and then transferred to a database once back in the office. The current system is outdated, clunky and time-consuming.
The new technology can also be used for inspections of trees as well as to report fallen or damaged ones. In Exeter, the City Council is responsible for some 8,000 trees in its parks, open spaces, in council house gardens and on local authority land.
Cllr Ollie Pearson, Lead Councillor for Enabling Services, said: "It's a privilege to be at the cutting edge of new technology and trialling an application that will not only save time and money for the Council but will also hopefully enable residents to be able to report trees when they come down or are damaged."