The council's social services department has around 4,000 staff places, but some teams have a vacancy rate as high as 30 per cent.
The first stage of the PR campaign now underway is an attempt to change perception of social work not just among the public and potential recruits, but also among social work teams themselves.
The next stage, to launch within weeks, is a PR and advertising campaign specifically to get information to potential recruits about getting involved with social work. This will target recent graduates and those considering a return to social work after a career break.
As part of the first phase of the campaign the council's PR and marketing team last week attended a conference of social work managers and directors in the city to stage workshops on branding, public perception and dealing with the media.
Martin Gavin, the council's social work media co-ordinator, said: 'There has been a tendency within the profession to come into work and put the grills up when it comes to the media. What we are saying is that there are good news stories there and it's important to let the public know that.'
The council, however, has refused to offer social work staff so-called 'golden hellos' or enhanced pay and conditions that other councils have used in an attempt to improve recruitment.
Gavin said the campaign has addressed this issue by attempting to convince potential recruits that training and 'the career-building know-how gained from working in a major city' outweigh enhanced pay packages being offered elsewhere.
He added that better deals offered by other councils simply move existing staff around boroughs and do little to attract new recruits.