"He did say to vote for Gary Johnson, didn't he? And that was 'vote your conscience,'" he told CNN's Chris Cuomo on "New Day." "I certainly would uphold the Constitution."
On Wednesday, Cruz upset many Republican National Convention attendees when he refused to endorse the party's nominee, Donald Trump, and told the crowd to "vote your conscience."
Johnson is just polling points from being able to appear on the presidential debate stages this fall.
"Thirteen percent in the polls. Oh my gosh. Looks like we're going to get in the presidential debate," he said. "Keeping in mind, just in the last six weeks, 13% is double what it was just six weeks ago."
Johnson said he thinks he'll get the 15% needed to make the debate stage because there's a lot of interest in him and his vice presidential nominee Bill Weld because of dissatisfaction with Donald Trump. A candidate must reach 15% in five polls selected by the Commission on Presidential Debates to participate in debates.
"I think Donald Trump alienates more than half of the Republicans," he said.
Johnson, who was speaking in Cleveland, said Republicans have repeatedly stopped him to express support for him.
"Like 1,000 people. Amazing. And not one single jab. You'd think I'd get a poke. At least one poke," he said. "Amazing. Really. Unbelievable. You would have figured a couple of 'Hey what are you doing?'"