Quaid and his wife Evi are seeking refugee status in Canada after fleeing over the border from the United States, claiming their lives were at risk.
The actor, who played a supporting role alongside Ledger in the Oscar-winning film Brokeback Mountain, said he was being hunted by a gang of Hollywood "star-whackers" who already had a long list of celebrity victims.
Heath Ledger is one of many actors named in Quaid's conspiracy theory.
"Up until a year ago Evi and I had never had any run-in with the law whatsoever," he said.
"We are not criminals nor are we fugitives from justice. Nor are we crazy. We are simply artists and filmmakers who are being racketeered on."
The brother of actor Dennis Quaid then broke down when he told a gathered media pack about how the criminal group had some of Hollywood's biggest names in its sights.
Actor Randy Quaid has fled to Canada, where he is seeking asylum. Photo: AP
"We believe there to be a malignant tumour of 'star-whackers' in Hollywood," he said.
"How many people do you know personally who have died suddenly and mysteriously in the last five years?
"I have personally known eight actors, all of whom I have worked with and was close to - Heath Ledger, Chris Penn, David Carradine among them.
"I believe these actors were whacked and I believe many others, such as Britney Spears, Lindsay Lohan and Mel Gibson, are being played to get at their money."
The couple are wanted in the United States on vandalism charges. The day after they arrived in Canada last Sunday, a California judge issued an arrest warrant for them after they failed to appear at a mandatory court hearing on charges they had been illegally squatting in a home they owned years ago.
Quaid was arrested in September on suspicion of burglary and entering a building without consent. Evi Quaid was booked on those charges, as well as resisting arrest.
This year, they were arrested on charges of failing to pay their bill at a California hotel. Evi Quaid was forced to pay $US10,500 in restitution in that case and she pleaded no contest to defrauding an innkeeper.
- WAtoday.com.au, with Reuters