The newly-elected congresswoman, known in particular for her radical climate change policy, encountered the man and his teenage son outside her Washington office.
Ms Ocasio-Cortez said the pair posted a note on the wall outside which read: “Trump supporters for Ocasio-Cortez”.
They introduced themselves and thanked the New York Democrat for her work, she said on Twitter.
She said she asked the man: “With all respect sir, how do you manage to support both of us at the same time?”
Alexandria Ocasio-Cortez - the Democratic congresswoman in pictures
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He said: “I’ve been saying for years that climate change is our most important crisis. You’re one of the only ones who‘s been willing to be decisive on it.”
Ms Ocasio-Cortez has vocally pushed for what she called a Green New Deal, a comprehensive plan of climate action.
She said the father added: “I like you. I can tell that you are genuine and fighting for us. You’re real and you get it.”
Ms Ocasio-Cortez said that she then thanked the family for their kindness,
In a further tweet she added: “Don’t let any politician, no matter the party, lecture you about what is ‘possible’ or ‘electable’.
“The forces getting in the way of solving our climate crisis are politicians themselves + lobbyists. It is the willingness to bend to corporate power – the same ones that use coal miners’ plights for a tax break, yet refuse to pay for those same miners’ healthcare for black lung.”
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