"To sign the petition" means to formally add your name or signature to a document or list that expresses support or a request for a specific cause, goal, or change. Full definition
Under the coalition's proposals MPs could be recalled if ten per cent of their constituents sign a petition calling for a by - election. (politics.co.uk)
Please sign the petition at the link above even if you have previously signed the federal government petition shown below the image on this page. (cedamia.org)