The US District Court here issued the summons on a complaint filed by New York-based Sikh for Justice (SFJ) and two alleged victims of the 1984 anti-Sikh riots.
The victims Babu Singh Dukhiya is based in Delhi and Mohender Singh is based in California.
The court has directed Bachchan to respond in 21 days after he is served with the summons.
Running into 35-pages, the complaint alleges that Bachchan instigated people for violence after the assassination of the then prime minister Indira Gandhi.
In the past several years, SFJ has unsuccessfully tried to drag several Indian leaders to US courts in the alleged human rights violations cases.