Tarantino's lawsuit accuses Gawker Media LLC of copyright infringement for posting a link to his 146-page script for a planned film called The Hateful Eight.
Gawker operates numerous sites and blogs and posted a link to Tarantino's script on its Defamer website last week.
An email sent to Gawker seeking comment wasn't immediately returned.
Tarantino's lawsuit filed today in a federal court in Los Angeles states that he planned to publish the script and has received substantial royalties and advances by doing so with past projects.
Tarantino has won two screenwriting Academy Awards.
The lawsuit was first reported by The Hollywood Reporter.
Tarantino blasted the leak last week in an interview with Deadline.com and said he would abandon the project as a film. His lawsuit states his damages as a result of the Gawker post will be more than one million dollars (£600,000).
The leak of Tarantino's script was initially limited to a few people, his lawsuit states, and The Hateful Eight script did not appear online until after Gawker posted an item encouraging anyone who had a copy to leak it to them.
Tarantino has won screenwriting Oscars for his films Pulp Fiction and Django Unchained. He also received best director Oscar nominations for Pulp Fiction and Inglourious Basterds.
In October 2012, former wrestler and reality TV star Hulk Hogan sued Gawker after it posted a video of him having sex with the wife of his best friend. The site complied with a judge's order in April to remove the video, but left a story and reader comments on its site.