It comes as new figures from Public Health England reveal that the variant - first identified in India - is around 60% more transmissible than the variant responsible for the winter wave of Covid-19 in the UK.
Mobile testing sites across the district have been set up - people do not need to book an appointment to get tested.
Sarah Muckle, Bradford Council’s Director of Public Health, said: "I would urge people to take the opportunity to get a test even if they don’t have any symptoms.
"We want to help stop the new Delta variant from spreading further and I would ask everyone, across all our communities to protect themselves and their families by getting tested. Tests are simple and you don’t need an appointment.
"When you’re offered the vaccination, both doses, please take it up as soon as you can to help reduce the spread of the virus. We all need to follow the guidelines and protect our local community."
The council have asked people to be "vigilant" for any Covid-19 symptoms whilst enhanced testing is in place.
People are also reminded to regularly wash their hands, use face coverings where required, keep their distance from others and to ventilate rooms with fresh air when meeting people indoors.
Testing sites in Bradford can be found at:
Centenary Square, Bradford
University of Bradford
Victoria Hall, Keighley
Pudsey Civic Centre car park
And in addition on weekdays at Flockton Road car park, Shipley Pool car park and Richard Dunn Sports Centre.