The call comes from the Fostering Network ahead of the Children and Young People’s Bill reaching its report stage in the House of Commons on October 8.
Teachers and childminders already have to register with Ofsted - and residential social workers are next in line to be registered with the General Social Care Council - but foster care remains the only child care profession where workers remain unregistered.
Fostering Network says registration with the General Social Care Council would also improve safeguards for children because it would allow for the introduction of a national code of conduct for foster carers, with raised expectations regarding continuing professional development.
Robert Tapsfield, chief executive of the Fostering Network, said: "Registration would ensure that foster carers get the status and recognition that their role demands and improve the respect and treatment they get from the other professionals they work with.
"At present, if a foster carer wants to change fostering service, they have to reapply. A central register would mean that foster carers would not have to be reapproved when they move and that there would be a central record of any concerns about their practice, which social workers could refer to."
The Fostering Network also wants to see a national roll out of pilot projects to enable young people in foster care to stay on with their foster carers until 21 if that is what they want and need.
The charity says there is no need for pilots as similar schemes already exist in some parts of the country and research shows that if a young person can stay on until 21 they are more likely to do well later in life.