It follows the city pioneering hydrogen buses and car club vehicles.
Aberdeen Taxis will run a one-year trial of the Hyundai ix35 hydrogen fuel cell car after the city council granted it a private hire taxi licence last month.
It has a range of 326 miles - more than three times that of many electric cars.
Refuelling takes about three minutes, and experts said hydrogen cars cost about half as much to run as petrol or diesel models..
Their fuel cells convert hydrogen into electricity for propulsion, with water vapour the only emissions.
There are already ten hydrogen buses operating in Aberdeen - the first in Europe.
The Co-wheels car club runs three hydrogen-powered Toyota Mirais and one Hyundai ix30.
A further nine hydrogen cars and four vans are operated in Aberdeen by the city council, NHS, Scottish Environment Protection Agency and social enterprise organisation Scarf.
Council communities, housing and infrastructure convener Yvonne Allan said: “As the first city in Scotland to have its own hydrogen taxi, this is an exciting opportunity for Aberdeen.
"Use of this vehicle as a private hire taxi will also allow citizens of Aberdeen the opportunity to travel in a hydrogen vehicle and broaden the understanding of the technology.
“The car, which emits only water vapour, is zero emission and can play a part in improving the air quality of our city."
The taxi was funded by the Scottish Government's Transport Scotland agency.
Transport minister Humza Yousaf said: “I’m delighted that Scotland’s first hydrogen taxi will be transporting customers in Aberdeen and showcasing the benefits that ultra-low emission hydrogen vehicles can bring.
“Hydrogen-fuelled vehicles play an important role in improving air quality and complement our vision for electric vehicles.
"This announcement reflects our ambitions to phase out the need for new petrol and diesel cars and vans by 2032.”
Aberdeen Taxis director Chris Douglas said: “Aberdeen Taxis have always been dedicated to embracing the newest technology and, alongside the hydrogen taxi, have developed a number of environmentally-friendly projects including electric taxis.
“We believe the smoothness and quietness of the hydrogen vehicle will be appreciated by not only drivers but also our passengers.
"We also believe that the environmental benefits of running pure hydrogen and electric vehicles will make a real difference for the people of Aberdeen.”
Supporters of the technology said if hydrogen is generated from intermittent renewable electricity sources, such as wind turbines, it could be stored indefinitely.
The power source could then be added to the natural gas grid and generate electricity at times of peak demand - as well as powering vehicles.
However, the IAM RoadSmart motoring group has said drivers must be assured of the safety of hydrogen
Policy and research director Neil Greig said: “Hydrogen cars must, as a minimum, meet the best crash protection standards that currently apply to traditional models.
“The key to their success, however, will be the speed with which a re-fuelling network can be run out."