The recommendation is one of 13 put forward by a 'Women in the Workplace' panel, which was tasked with looking at the council's procedures to deal with harassment.
The panel's chair called the report "an important piece of work", and said she believed the suggestions would improve life for female workers at the council.
Councillors will decide whether or not to adopt the recommendations in the new year.
Among the recommendations put forward by the panel was for a support network to be set up for harassment victims, which would take a similar form to the mental health first aiders already available to council staff.
The authority's also been urged to include "appropriate warnings" around harassment on its IT and communication systems and to roll out more training for managers around inclusive behaviour.
Conservative councillor Annemarie Glover, who chaired the panel, said discussions around the issue during its enquiries had been "constructive and frank".
She said: "I think the recommendations will strengthen the policies that are already there and give them a little bit more substance.
"It's been a very important piece of work, very informative and I'm very proud of it.
"Having a women's advocate in particular, in the same way the council already has mental health advocates, I feel will have a really positive impact."
Councillor Glover said Covid restrictions had limited her access to the council's female staff, to whom she'd hoped to speak to get a picture of what their working lives were like.
But she said she had managed to speak to a wide "cross section" of people, including trade unions, who contributed significantly to the final report.
She added: "Society's still got some way to go.
"Having a situation where women don't feel safe walking the streets, that's something that needs addressing.
"As any parent with a daughter does, I worry about that."
Local Democracy Reporting Service