Sheen's dad has previously won a Golden Globe, as well as multiple SAG awards and an Emmy, but has yet to receive Hollywood's top prize.
His son is now rallying behind him, insisting the West Wing star has given "the best performance of his career" in The Way, which was written and directed by another family member, Emilio Estevez.
The former Two and a Half Men actor is hoping his last ditch appeal will help garner his dad some support before votes for nominations close next Friday.
In a post on Twitter.com, Sheen writes: "The time is now! My father, Martin Sheen, is currently starring in The Way, written and directed by my brother, Emilio Estevez...! And... he has given the best performance of his career!
"Academy Award ballots are due next Friday and we need to insure (sic) that Martin gets nominated. Help spread the word... Martin Sheen Oscar!"
See Martin Sheen in The Way in the trailer below:
SUBSCRIBE AND FOLLOW
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements.Learn more