James McAvoy Sr, 55, and Donald McAvoy, 24, were arrested on December 5 and made a private appearance at Glasgow Sheriff Court.
They are charged with being concerned in the supply of class A drug cocaine at a flat in Kinfauns Drive, Drumchapel.
Both men made no plea or declaration when they appeared before sheriff Janys Scott and both have been granted bail.
James Jr, 34, originally from Drumchapel, has had no contact with his father since childhood and has never met his half-brother.
The Filth star was crowned best actor at the Moet Independent Film Awards earlier this month for his role in the film.
In a previous interview, James Sr said: "It has been hard on me not being in his life, but I'm just glad that he seems happy.
"I hope one day he'll get in touch. I was amazed he's done so well."
The father said he thinks his son had hopes that his parents would sort things out after they split, but James Sr moved in with his new partner, who is Donald's mother.
James Sr added: "He started refusing to see me because he didn't like Mary. In the end I took a step back rather than upset him."