Davis was convicted in 1991 of fatally shooting off-duty police officer Mark MacPhail in 1989, despite prosecutors failing to find a murder weapon or any physical evidence linking him to the crime.
His lawyers, who have maintained their client is a victim of mistaken identity, had a plea for clemency rejected on Tuesday (20Sep11) and one final appeal, filed on Wednesday morning in a bid to prevent Davis being killed by lethal injection, was also denied.
A host of celebrities, including hip-hop mogul Russell Simmons, country singer Chely Wright and author Salman Rushdie, voiced their disbelief at the clemency denial and now Farrow has called on government officials in Georgia to step in and intervene.
In a series of posts on Twitter.com, she writes, "GA (Georgia) prison medical staff shd (should) stay home (on Wednesday). Grievous errors in case against Troy Davis. Too much doubt for execution to be carried out.
"Georgia gov please don't execute Troy Davis... Surely we, as a nation - are better than this."
Meanwhile, rapper Big Boi has taken it upon himself to organise a march outside government offices in Jackson, Georgia to protest the execution.
Calling on fans to join him, he 'Tweets', "We don't need a trending topic (on Twitter), we need boots on the ground, meet me in Jackson Georgia 40 miles outside Atlanta!!!"
Socialite Kim Kardashian has also used her Twitter blog to express her disgust at the judicial system, writing, "I want to vent about the execution of Troy Davis! He is getting the death penalty tonight but I believe he is innocent!!! Too much doubt.
"All he wants is a polygraph test 2 (sic) prove he's innocent & the judicial system can't give that to him?... Everyone 'Google' Troy Davis & read his story! No one should die by lethal injection when there is this much doubt! Help save Troy Davis"