The California Democrat, who has endorsed Hillary Clinton for president, has a history with the former Hewlett-Packard chief executive -- she defeated Fiorina in 2010 to keep her Senate seat. After the announcement, Boxer tweeted that Cruz "talks tough on Iran, but his 'running mate' was soft on Iran when she skirted the law to sell them computer parts."
Boxer was referencing a Republican presidential debate statement by Fiorina about being unaware that during her tenure at HP the company was selling printers to Iran at a time when U.S. companies weren't allowed to do so.
The Cruz campaign did not immediately respond to CNN request for comment.
Boxer continued her Twitter critique of Fiorina by writing, "Slogan idea for the Cruz/Fiorina 'ticket': 'Mean & Meaner'"
After that Boxer tweeted, "Cruz/Fiorina= a perfect match. He wants to ship immigrants out and she's a champion at shipping jobs out."
Boxer then referenced her reelection fight against Fiorina, now a Virginia resident, writing, "Cruz thinks Fiorina will help in California. Maybe he doesn't know Carly left after she lost by a million votes?"
In her reelection bid against Fiorina in 2010, Boxer won 52% to 42%
Boxer, who is retiring from Congress after the fall elections, ended her Twitter spree by writing, "I predict that the latest @CarlyFiorina merger will be as successful as her last one."
That tweet appears to be a dig at the rough merger between HP and Compaq that occurred during her tenure, which resulted in tens of thousands of employees being laid off, jobs being sent abroad and the company's stock falling by some 50%.