The group of Republicans say they will object to the 6 January certification of Joe Biden’s win unless there is an emergency 10-day audit of the results by an election commission.
Mr Cruz is being joined by Ron Johnson, James Lankford, Steve Daines, John Kennedy, Marsha Blackburn, Mike Braun, as well as Senators.-elect Cynthia Lummis, Roger Marshall, Bill Hagerty, and Tommy Tuberville.
Together the 11 senators they say that the election “featured unprecedented allegations of voter fraud and illegal conduct”. Separately, GOP senator Josh Hawley is also to seek a challenge.
“Voter fraud has posed a persistent challenge in our elections, although its breadth and scope are disputed,” the politicians said in a statement.
“By any measure, the allegations of fraud and irregularities in the 2020 election exceed any in our lifetimes.”
Despite Donald Trump’s wild claims of voter fraud, his legal team, which includes former New York mayor Rudy Giuliani, have not presented any credible evidence in lawsuits that have been overwhelmingly rejected by judges.
The election results have been ratified by each and every state and the former head of the federal government’s cyber security unit described it as the “most secure” election in US history.
The outgoing president has also failed to get any case to the Supreme Court, which has refused to be drawn into his attempt to cling to power.
This is a separate effort from that of Mr Hawley, who says he will object to the alleged failure of some states to follow their own election laws.
Mr Trump has refused to concede the election to Mr Biden, despite a strong of courtroom defeats in battleground states across the US.
Mr Biden flipped Arizona and Georgia to take him past the 270 electoral college votes needed to secure the White House, and he easily beat Mr Trump in the popular vote.
The senators and sentors-elect claim that there is a historical track record for Congress to appoint an electoral commission to audit results where they are disputed.
They cite as precedent the 1877 contest between Samuel Hayes and Rutherford Hayes, where there were allegations of fraud in several states.
“In 1877, Congress did not ignore those allegations, nor did the media simply dismiss those raising them as radicals trying to undermine democracy,” they said.
“Instead, Congress appointed an Electoral Commission, consisting of five Senators, five House Members, and five Supreme Court Justices, to consider and resolve the disputed returns.”
The move by Mr Cruz and his group comes after it was predicted that up to 140 Republican members of the House fo Representatives could vote against counting the electoral college votes.
Mr Trump’s supporters have virtually no chance of changing the results of the election but may be able to hold up certification for several hours.
Senate majority leader Mitch McConnell has privately urged Republicans not to object to the counting of the votes.