The Dunfermline MSP, 71, who was expelled from the SNP after the allegations were revealed in the Sunday Herald on March 3 last year, was yesterday convicted of 24 charges spanning almost 30 years.
He will be sentenced on September 20. The maximum sentence he could face is a year in jail.
Under the Representation Of The People Act, an MSP must be jailed for more than a year to be disqualified from serving at Holyrood.
Lily Greenan, manager of Scottish Women's Aid, said: "He has been convicted of three decades of offences against women.
"He is not a fit person to hold public office and he should be required to step down as an MSP.
"It may be the rules need to be rethought and have regard to the nature of the offences, not just the length of the sentence.
"Taken individually the offences may appear minor, as is often the case with domestic abuse, but looking at the whole pattern, people's liberty, their ability to live their lives, has been constrained by a controlling and abusive partner."
The Representation Of The People Act would have to be amended at Westminster. However, Holyrood may have the power to introduce its own "recall" law as a means of forcing a by-election.
First Minister Alex Salmond, whose party Walker had represented, said: "Mr Walker has been convicted of extremely serious offences. Someone convicted of these offences is not fit to be a public representative and therefore he should stand down from the Scottish Parliament and allow the people of Dunfermline to elect a new MSP."
Labour MSP Claire Baker said: "Bill Walker should stand down now. His vile conduct over many years will disgust Scots and shames the Scottish Parliament."
Willie Rennie, leader of the Scottish Liberal Democrats, said: "What sort of message would it send to victims of domestic abuse if Bill Walker was allowed to keep his seat?"
Walker, of Alloa, who was a Fife councillor before entering Holyrood, has refused to resign since the allegations were revealed in March 2012. He was suspended by the SNP and expelled a month later but continued to sit as an Independent.
At Edinburgh Sheriff Court yesterday, Sheriff Katherine Mackie said: "There was evidence showing the accused to be controlling, domineering, demeaning and belittling towards the three complainers, his former wives."
She said she found Walker's ex-wives "credible and reliable" witnesses, but not the MSP.
Walker was found guilty of assaulting his first wife Maureen Traquair, 66, on three separate occasions in the 1960s and 1980s.
On one occasion, he punched her in the face two weeks before their wedding day in January 1967, giving her a black eye.
The MSP was found guilty of assaulting his second wife Anne Gruber, 71, 15 times between 1978 and 1984. He was also found guilty of assaulting Mrs Gruber's daughter Anne Louise Paterson, when she was 16 in 1978. He committed a breach of the peace by brandishing an air rifle at her house.
Walker was also convicted of four assaults on his third wife Diana Walker, 61, three of which involved slapping or punching her on the face.