The civil lawsuit, filed in federal court in Washington, alleges that the attack, which left five dead including a police officer, was a "direct and foreseeable consequence" of unlawful actions by Trump, Giuliani, Trump's eldest son, Donald Trump Jr., Republican congressman Mo Brooks and others.
"As such, the Defendants are responsible for the injury and destruction that followed," said Representative Eric Swalwell, who filed the lawsuit.
The lawsuit draws on evidence from the impeachment trial, including Trump tweets leading up to the attack, and details the former president's efforts to pressure state lawmakers to halt President Joe Biden's victory.
Trump spokesman Jason Miller said in a statement that Swalwell "is a low-life with no credibility."
Giuliani did not immediately respond to a request for comment. A Brooks spokesman also did not immediately respond to a request for comment.
Representative Bennie Thompson, a Democrat who chairs the House of Representatives Homeland Security Committee, last month filed a lawsuit accusing Trump, Giuliani and two right-wing groups of conspiring to incite the riot.
Swalwell's lawsuit alleges Trump and his allies broke a US law that prohibits conspiracies to violate civil rights. The lawsuit seeks monetary damages against the defendants, including punitive damages.
Jessica Levinson, a professor at Loyola Law School in Los Angeles, said Swalwell's lawsuit was "not a slam dunk" but might eventually result in Trump sitting for an interview under oath.
"As with so many suits against Trump, the name of the game may be to keep the suit going long enough to take depositions and obtain discovery," Levinson said.