The disgraced comedian, who is serving time behind bars for drugging and raping Andrea Constand in 2004, shared the bizarre message on his official Twitter and Instagram accounts.
It began: "Hey, Hey, Hey...It's America's Dad."
The tweet appears to be in reference to Cosby's role as family man Cliff Huxtable on the top-rated The Cosby Show from 1984 to 1992, for which he became known as "America's Dad".
"I know it's late, but to all of the Dads... It's an honour to be called a Father," he continued.
"So let's make today a renewed oath to fulfilling our purpose - strengthening our families and communities."
The message was followed by several hashtags, including #HappyFathersDay, #RenewedOathToOurFamily and #FarFromFinished.
While it's unclear whether Cosby himself, who is currently incarcerated in a Pennsylvania prison, had a hand in writing the post, it was poorly received by users online, who slammed the 81-year-old as an "a...hole".
"Strengthen families by not being unfaithful to your wife, by not treating young women like they're on the menu, and by not being a bad example to young men," tweeted one user.
While another commented, "First OJ, now this? Blocked in a New York Minute."
Former American football player O.J. Simpson launched his own Twitter account on Saturday in a bid to "challenge the bulls...", and shared Father's Day message to refute "bogus" rumours he is Khloe Kardashian's biological father.
Reflecting on both stars' messages, a third user joked: "Father's day is cancelled."