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Ted Cruz has earned a defector from the shuttered campaign of Marco Rubio: Phil Gramm, the former Texas senator once cited by Mr. Cruz as “the senator I most admire.”

Mr. Gramm, 73, who began his career in Congress as a Democrat and became a top economic adviser to John McCain’s 2008 presidential campaign, called Mr. Cruz “a fearless leader and fighter for conservatives.”

Mr. Cruz, a Texas senator, praised Mr. Gramm for his opposition to health care legislation during President Bill Clinton’s administration. “Phil stood firm and unequivocally with the American people,” Mr. Cruz said.

The endorsement comes as Mr. Cruz hopes to consolidate support among Republicans opposed to Donald J. Trump. In recent weeks, he has attracted the endorsements of Carly Fiorina, Senator Mike Lee of Utah and Senator Lindsey Graham of South Carolina, who was once a bitter foe.

Last year, when Mr. Gramm, whose Senate term ended in 2002, signaled his support for Mr. Rubio, he suggested that Mr. Trump would nonetheless win the Republican nomination.