The standalone clip, entitled 3am, has been posted on YouTube.
Republican candidate Donald Trump is seen with a copy of a book called Great Speeches by A. Hitler in the video.
When Homer signals that he might vote for Trump, Marge says: "If that's your vote, I question whether I can ever be with you again."
Homer replies: "And that's how I became a Democrat."
Clinton and Trump are set to face each other in the US presidential election, which takes place on 8 November.
The Simpsons' discussion comes about when Marge says that she "can't make love until I've decided who to vote for".
The narrator then poses the question: "It's 3am and the phone is ringing in the White House - who do you want to answer that call?"
The question is a reference to Hillary Clinton's political campaign of 2008, which ran an ad featuring a ringing phone at 3am, asking Americans who they wanted leading their country during a time of crisis.
Both Clinton and Trump are then seen responding to such a phone call.
Trump responds by saying: "Not now, I'm on Twitter."
He then orders an aide to: "Put my name on the Lincoln memorial, disband Nato... and make me some scrambled eggs on gold plates."
Bill Clinton is seen initially answering the phone with: "The situation room? I'll be right there."
His face then falls as he hands the phone to Hillary, saying: "Oh, it's for you."
His wife replies: "Yes, from now on, it's always for me."
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Marge and Homer Simpson agree to vote for Hillary Clinton in the forthcoming US election in a new video clip released by 20th Century Fox.