Aikman, 29, was diagnosed with motor neurone disease earlier this year. All proceeds of the challenge are going to the Motor Neurone Disease Association.
The Deputy First Minister accepted the challenge, tweeting: "@GordonAikman challenge accepted...watch this space..."
Alex Salmond was nominated by actor James McAvoy to accept the challenge. He said he plans to accept it.
Alastair Darling did the challenge on Friday after also being nominated by McAvoy.