The former Respect MP says he would be a "formidable" representative for the area.
Ms Ferrier has been under pressure to stand down after it emerged she travelled to London to sit in the House of Commons and then returned to Scotland while infected with Covid-19.
She was suspended by the SNP and Nicola Sturgeon has been among those leading the calls for her to resign as an MP. But she has refused to go and made her first Commons appearance since the row last week.
A Parliamentary Standards & Privileges committee probe is already underway into her conduct. If it decides to suspend Ms Ferrier for ten days, it would trigger a recall petition requiring 8,000 signatures from the area to bring about a by-election.
Mr Galloway heads up the anti-independence Alliance 4 Unity party that will stand candidates in next May's Holyrood election.
He has now launched a crowdfunder with a target of raising £100,000 to stand in Rutherglen and Hamilton West.
“When Margaret Ferrier made the idiotic decision to become a coronavirus super-spreader, I led from the front - starting a petition with over 10,000 signatures to date, demanding she resign," Mr Galloway said.
"It is abundantly clear that the Parliamentary Standards committee should suspend Ferrier, triggering a recall petition. I could get the necessary 8,000 signatures to force a by-election in a single weekend, if not an afternoon, such is the strength of feeling in Rutherglen and Hamilton West.
“I have dedicated my life to advocating for Scotland in Parliament, spending 18 years representing neighbouring Glasgow in the House of Commons.
“With a proven track record in Parliament, I hope constituents agree that I will be a formidable MP for the area.”
Ms Ferrier travelled to London from Glasgow in September after feeling unwell and having had a Covid test. She was informed while in London that she had tested positive, but still travelled home by train, risking exposure to others.
She made her first appearance in the Commons by video link last week since the furore erupted two months ago, with an urgent question on the situation in Hong Kong.