Lawsuits over software have become commonplace in recent years, and some "patent trolls" compile a large portfolio of patents with the intent of threatening to sue other companies rather than actually developing any products.
Proponents of software patents argue they are needed to ensure that software developers can profit from their innovations.
President Obama signed a law overhauling the patent system earlier this month, but the measure did not revoke software patents.
The petition currently has nearly 11,000 signatures. The White House has promised to send any petitions that pass 5,000 signatures within 30 days to the appropriate policy analysts and issue a formal response.
Ending software patents is currently the sixth-most popular petition on the White House's website.
Legalizing marijuana remains the most popular petition, with more than 35,000 signatures.