The Better Together leader posted a picture of himself being drenched in icy water after he and First Minister Alex Salmond were nominated by the Scottish actor.
The social media craze is aimed at raising awareness and money for the neurodegenerative disease ALS, or motor neurone disease.
Mr Darling thanked McAvoy and tweeted a link to www.gordonsfightback.com, an awareness-raising site set up by Better Together director of research Gordon Aikman.
Mr Aikman publicly revealed he is dying of the disease in a powerful article in the Scotland on Sunday newspaper in June.
The First Minister has also accepted McAvoy's challenge.
Mr Salmond said: "I'm always up for any challenge, and I'm game for this one. It will invigorate me for the next month of campaigning - but the Scottish media should be careful what they wish for, as I get to nominate who's next for the ice bucket!"
In his video, X-Men star McAvoy said: "As it is the year of the Scottish referendum on independence, I'd like to nominate our political champions Alistair Darling and Alex Salmond to do their very worst."
As a bucket of icy water is poured over his head, he adds: "Alex, Alistair, you've got 24 hours."
McAvoy said he was nominated for the challenge by Chelsea manager Jose Mourinho.
Former US president George Bush, actress Gwyneth Paltrow and footballer David Beckham are among a host of well-known faces that have taken the plunge.
McAvoy, from Glasgow, has previously said he is "anti-political" when it comes to independence.
In an interview in May, he said: "I will go with whatever way my country votes, but I don't know which way I want to go yet."