The designer rode on the tank in protest over the 27 licences which have been issued in the North and Midlands.
Dame Vivienne said: "The public will not take it lying down and will fight tooth and nail."
The tank, which was parked outside the PM's home, was accompanied by anti-fracking campaigners wearing masks.
The group included grandmothers and their grandchildren from Lancashire, which is affected by the latest round of fracking licences.
Fracking, an underground drilling process, involves water, chemicals and sand injected into rock at high pressure.
Dame Vivienne said the threat of "toxic, life threatening" chemicals had led to a "declaration of war on fracking".
According to the fashion designer, the chemicals used to extract shale gas from rocks can contaminate water and cause health problems.
The Department of Energy and Climate Change has said it will not allow hazardous operations when it comes to fracking.
It said any chemicals used were subject to assessment by the Environment Agency which will not permit their use if there is a risk to the environment or people's health.
Under the licences, fracking firms could run shale gas pipelines on private land without getting prior permission.
"Cameron plans to force householders to surrender their land and endure fracking underneath their homes. Britons no longer have any choice but to fight back", Dame Vivienne said.
The government has released a map showing 27 fracking licenses in areas in northern England and the Midlands.
It is not known if Mr Cameron or his family were at their home during the protest.
Dame Vivienne Westwood has ridden in a tank to David Cameron's home in Witney to campaign against the government's fracking plans.