In the lawsuit, filed Wednesday in California Superior Court in Los Angeles, the “White House Down” actor also accused the user -- known as “Abe List” -- of invasion of privacy by false light.
Woods, 68, says in the court papers that he is not -- and never has been -- a cocaine addict, adding that Abe List must pay for the “malicious” online campaign and the resulting damage to the actor’s reputation which caused Woods “shame, mortification, hurt feelings, emotional distress, embarrassment, humiliation and injury to his peace of mind."
Woods’ court papers refer to the Twitter poster as “a cowardly individual.”
According to the lawsuit, Abe List user started harassing Woods online in December, calling him “clown boy” and “scum,” among other derogatory terms. It was on July 15 that Abe List tweeted “cocaine addict James Woods still sniffing and spouting,” the court papers allege.
Abe List has since deleted his Twitter account, but Woods says in his lawsuit that he intends to unmask the individual behind the account.
The false statement about cocaine use were seen by Abe List’s thousands of followers and possibly by Wood’s 238,512 Twitter followers, the court papers allege, also noting that the statements were accessible to anyone doing a Google search.
“The false statement has been published for hundreds of thousands of people to see, which includes friends, family, potential employers, business associates, colleagues and fans of Woods,” the lawsuit says.
The false statement “clearly exposes Woods to hatred, contempt, ridicule” which causes Woods to be “shunned or avoided, and has a tendency to injure him in his personal life and occupation,” the lawsuit also says.
Woods declined to comment when contacted by ABC News.
A social media law expert says Woods may have a tough case with his lawsuit.
"This is going to be very difficult for James Woods to win because, as a public figure, he's going to have to prove actual malice," Bradley Shear told ABC News. "You have to determine what the person's intent was...the only way to do that is to actually track down the individual."
Woods is not the first celebrity to have taken a stand against hostile Twitter users.
In March, actress Ashley Judd was on the receiving end of vulgar messages and threats while she tweeted during a college basketball game.
At the time, she pledged to press charges against the authors of the abusive tweets. Although it is unclear if Judd has taken any concrete legal action at this time, Shear says lawsuits over online statements are the wave of the future.
"This is literally the tip of the iceberg," he said. "You're going to have more cases where people will be suing others based upon intentionally defamatory statements made about others online."