The New York congresswoman shared a series of pictures, taken by New York Times photographer Tom Brenner, capturing her and Mr Connolly during a hearing recess in Washington.
Images show the pair in heated discussion until the final photograph, in which they are exchanging glances while smiling at each other.
“The last photo in this panel it’s like @GerryConnolly and I are in a road trip buddy comedy or something,” Ms Ocasio-Cortez wrote on Twitter.
Other users of the social media site chimed in to say how they thought a show featuring the two could play out.
“It’s like the last freeze frame shot on a tv sitcom about a couple of mismatched politicians – she’s a young upstart/ he’s a veteran – and together they’re ‘Takin’ the House’!” one wrote.
“This looks like the stills used in the intro to a late 80’s sitcom about a couple of mismatched leads,” another added.