Earlier, Cruz appeared on the program as news was breaking about Apple CEO Tim Cook announcing he's gay.
Read MoreI'm grateful Tim Cook said he's gay: Barney Frank
"I support marriage between one man and one woman," Cruz said in the "Squawk Box" interview. "And I support the Constitution letting each state decide each marriage law consistent with the values of their citizens."
He added, "If the citizens of California decide they want to allow gay marriage, that's a decision for them."
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In response, Frank said: "Ted Cruz is one of the most conservative people in American politics. He just made a very important statement that you ran on the air, in which he said, 'If a state wants to have same-sex marriage, that's OK.' That is an advance over the conservative position of just 10 years ago."