Councillor Julie Ford said she was “saddened, shocked, and angry” at the player being brought to Stark’s Park.
Goodwillie was ruled to be a rapist in a civil court case in 2016, but never faced a criminal trial.
Cllr Ford - whose father Nigel is a former Rovers’ director - has written to Steve Grimmond, chief executive, asking the local authority to formally review its relationship with the Kirkcaldy club.
She said: "As someone who grew up at Stark’s Park while my dad was a director, to spending my days looking out onto the stadium while at school, to recently taking my daughter every week for her girls only football training, I am saddened, shocked, and angry at the club's decision to sign David Goodwillie.
“While we are trying to encourage more girls and young women into football, and show that this is no longer a sport reserved to only men, this signing flies in the face of that message.
“It shows that there is still a 'boys club' mentality among club boardrooms and that the lives and experiences of women are quickly disregarded when pound signs and promotion look to be for the taking.
“I have asked that the chief executive updates all elected members of any relationship that Fife Council has with Raith Rovers so that a review - if necessary - can be taken into our future relationship with it.”
The comments came as politicians spoke out on the controversy.
First Minister Nicola Sturgeon backed crime writer and lifelong Rovers fan Val McDermid’s stance on the signing, applauding those who had spoken out against the move for being “principled”.
Former Prime Minister Gordon Brown, also a well-known supporter of the club, said he "cannot support this signing", adding that he condemned rape and all violence against women.
"Because of the number of recent examples across football, I urge the football authorities to set out a policy to address cases of violence like this."
Kirkcaldy area councillor Kathleen Leslie echoed those sentiments.
She said: “Raith Rovers need to do some soul searching and consider the impact this will have not only on their fanbase but what message they are sending out to the wider community.
“I am particularly thinking of what this says to girls and young women who are interested in taking up football professionally and who may be involved with the club.
“Violent crimes against women are on the rise and this signing makes me very uncomfortable."
Claire Baker, Labour MSP, believes Raith should reconsider its decision.
“Fans are right to be angry with this signing, which is a huge error of judgement. Raith Rovers FC is a key part of its local community, a club with a significant youth fan base and with women’s and girls’ teams.
“This signing sends out entirely the wrong message to its supporters and the wider community.
“Raith Rovers need to review this decision urgently.”
Kirkcaldy MSP David Torrance expressed his concern on social media on Monday.
He posted: “As a lifelong supporter of Raith Rovers, was today’s signing good for the club? No it wasn’t.
“Was it morally right? No it wasn’t.