The campaigner, who calls himself Des Curley, is promising to protest for a day outside the regulator's offices if 30 other people sign up by the end of this year. So far, 16 have done so.
His promise is hosted by Pledge Bank, a website on which people promise to carry out actions if others join them.
In his pledge, Curley writes: "Individuals and companies should stop sponsoring charities that do not have complaints procedures to protect those they claim to serve."
A spokeswoman for the Charity Commission said: "Legally, charities don't have to have complaints procedures, but they are a useful way to keep step with users' needs."