Walker was jailed for 12 months last September after being found guilty of 23 assaults and one breach of the peace that spanned decades.
There will be a hearing before three judges in the Appeal Court in Edinburgh on April 17.
Sheriff Kathrine Mackie, who heard the two-week trial at Edinburgh Sheriff Court last year, said Walker showed ''contempt'' for his victims as she imposed the maximum sentence available to the court.
She found Walker guilty of assaulting his first wife Maureen Traquair on three separate occasions in the 1960s and 1980s.
On one occasion he punched her in the face, giving her a black eye two weeks before they married in January 1967.
He was convicted of assaulting his second wife, Anne Gruber, 15 times between 1978 and 1984. On various occasions Mrs Gruber was punched, slapped, kicked and pushed to the ground.
He spat on her face, threw household items at her, threatened to pour hot coffee over her and pulled her hair. He also breached the peace by leaping into Mrs Gruber's home brandishing an air rifle.
Walker, of Alloa in Clackmannanshire, was also found guilty of assaulting and injuring Mrs Gruber's 16-year-old daughter, Anne Louise Paterson, by repeatedly striking her on the head with a saucepan in 1978.
The disgraced politician, 71, was also found guilty of four assaults on his third wife Diana Walker, three of which involved slapping or punching her on the face. The attacks happened between June 1988 and January 1995.
Walker's crimes were committed at addresses in Edinburgh, Stirling, Midlothian and Alloa between 1967 and 1995.
The former SNP MSP, who was suspended and later expelled from the party after the allegations surfaced in March 2012, denied all the charges.
He claimed he was the victim of ''smearing'' and that his ex-wives colluded to accuse him of domestic violence.