Rangarajan was born on May 12, 1952 in a family of Zamindars and active politicians of Thiruchengode. His grandfather Paramasiva Subbarayan was the Chief Minister of Madras province from 1925 to 1926 and a Cabinet Minister under later Governments. Rangarajan's father Mohan Kumaramangalam was an important theorist and organiser of the undivided Communist Party of India. His mother Kalyani Mukherjee was the niece of Ajoy Mukherjee, sometime Chief Minister of West Bengal, and of Biswanath Mukherjee, husband of the communist ideologue and parliamentarian Geeta Mukherjee.
Rangarajan was deeply involved in student politics right from the earliest stages and he was one of the founding members and the first president of the National Students Union of India (NSUI). Prime Minister Indira Gandhi, called him to take up this post after going through due process. By 1973, he was elected a member of the All India Congress Committee. In 1977, on obtaining a degree from Kirori Mal College, Delhi University, he moved to Madras to practice in labour law. Rangarajan was asked by his very dear friend, soon-to-be-Prime Minister Rajiv Gandhi, to play an active role in politics. He contested and won the 1984 elections from Salem Lok Sabha constituency.
P.V. Narasimha Rao appointed him Minister of State for Law, Justice and Company Affairs in July 1991. Rangarajan saw the government as a corrupt congress regime. In a letter to the President he raised several issues with regards to corruption allegedly purported by the Prime Minister based on documents he had in his possession and that formed the basis of the Vohra Committee report. In this letter he even asked the President to ask the Prime Minister to step down and face an investigation against the charges.
In late 1993, Rangarajan resigned as Cabinet Minister. In May 1995, Rangarajan resigned from the primary membership of the Indian National Congress and along with Arjun Singh, N.D. Tiwari, Sheila Dixit and others, founded the Congress(T). However, Rangarajan lost his seat in the 1996 Parliamentary elections during which his new party suffered a crushing defeat.
In December 1997, Rangarajan joined the Bharatiya Janata Party. He won from the Tiruchirapalli Lok Sabha constituency in 1998 and 1999 and became one of the torch-bearers of the BJP in Tamil Nadu. He served with distinction as the Union Minister for Power and Parliamentary Affairs, holding additional charge of Law, Justice and Company Affairs, and Mines, in the Second Vajpayee Ministry from 1998 to 1999 and in the Third Vajpayee Ministry from 1999 until his death in 2000.
He is remembered as one of the most charismatic and brilliant leaders in post independent India, Ranga was loved and respected across party lines. His capacity to get bills passed in parliament was unmatched, because of this unique quality.
Rangarajan died on August 23, 2000 at the All India Institute of Medical Sciences at the age of 48 as a result of acute myeloid leukemia (blood cancer).