RCT originated in Amnesty International's first medical group, which was established in 1974 – one year after Amnesty had urged the medical profession all over the world to help fight torture. Back then, no systematic knowledge existed on torture and the after-effects of torture. The main aim of the group was, by means of systematic examinations, to demonstrate that the victims had been subjected to torture. By these examinations it was documented that people in many countries had been subjected to torture, and severe after-effects of the torture were demonstrated.

One of the strongest advocates was Inge Genefke, MD, who in 1982 initiated the establishment of RCT.

RCT was an independent organisation that was housed at the National Hospital of Denmark. This location enabled the treatment or hospitalisation of torture survivors at the hospital. Physicians, nurses, physiotherapists and other members of the medical profession soon realised that treating and nursing torture survivors often presented special problems that called for specialised and multidisciplinary treatment.

In 1984, when RCT moved to a villa next to the National Hospital of Denmark, the main aim of the organisation was to treat and rehabilitate torture survivors who were refugees in Denmark. The medical professionals worked to alleviate the mental and physical after-effects of torture by interdisciplinary interventions, the main emphasis of which lay on medical rehabilitation.

Furthermore, the organisation initiated education of Danish and foreign health professionals, undertook research in torture and the after-effects of torture and established an international documentation centre.

To meet the growing demand for rehabilitation of torture survivors the world over, the International Rehabilitation Council for Torture Victims (IRCT) was formed in 1985, initially as a department of RCT. In 1997, RCT and IRCT were separated into two independent organisations and IRCT has now become an international umbrella organisation for rehabilitation centres and organisations worldwide.

Today, RCT is part of a global network of human rights organisations fighting torture and other forms of organised violence. RCT's field of activity is the rehabilitation of torture survivors in Denmark, international co-operation with partners in a number of countries (in Latin America, Asia, Africa, the Middle East and East Europe), research, education and advocacy.