One of the signatories is Manal al-Sharif, who was arrested in May 2011 after posting a Youtube video of herself at the wheel of a car. The activist was freed a few days later while another woman, Sheima Jastaniah, who was sentenced to 10 lashes for defying the ban, was pardoned by the King in November last year.
Since then, their example has been followed by hundreds of Saudi women, dozens of whom have been arrested and freed only after being forced to sign a statement promising that they would not repeat their gesture of defiance.
The petition, which its promoters say has already gathered hundreds of signatures, asks the sovereign to support the "I will drive my car" campaign, saying that the right is recognised to women "by all religions and national and international laws", but denied only on the basis of "customs and traditions that do not derive from God".
As a first step, the petition asks for the right to drive to be applied to women who gained their licences in nearby countries, and for "driving schools for women" to be opened inside Saudi Arabia.
"We neither cooperate with any organisation or international body nor represent a political party or opposition and we do not want to begin a public protest," the scheme's promoters say. "We ask only that every woman needing to move around for her daily duties and who does not have a man to help her be allowed to help herself".
Women in Saudi Arabia today who need to use a car must either do so with a driver or with a male relative driving for them. (ANSAmed).