Ramaswami came from one of the leading sports families in India. He was the youngest son of Buchi Babu Naidu, often considered the father of Indian cricket in Madras. His two brothers, son and four nephews all played first class cricket.
When the only brother of his mother died young, Ramaswami was given in adoption to his maternal grandfather, which led to his family name being different from that of his brothers .
He studied in Wesley High School, Wesley College and the Presidency. On one occasion while at Wesley, he put on more than 200 runs for the last wicket to win a match after his team was 50 for nine, himself scoring 188*.
He joined Cambridge University in 1919 where he studied until 1923. In the summer of 1920, he won singles the Doherty Cup tournament open to all students in the university. He won a 'half blue' that year, representing Cambridge in the doubles, and earned a blue in 1921. On a tour of Holland, he won the singles and them,, doubles, partnering S. M. Hadi - another future first class cricketer.
In 1922, Ramaswami represented India in the Davis Cup with Dr. A. H. Fyzee and A. A. Fayzee. India defeated Romania in the first round at Bristol but lost to Spain in Beckenham. Ramaswami played only in the doubles partnering Dr. Fayzee and won both his matches. The Spanish pair of Comte de Gomar and Flaquer, whom they beat in five sets, went on to play the doubles finals at Wimbledon in 1923. In 1922, Ramaswami took part in Wimbledon, reaching the second round.
Ramaswami is one of the two Indian cricketing double internationals, the others being M. J. Gopalan.
Ramaswami returned to Madras in January 1924 and joined the Agricultural Department as an Officer. He served in different parts of the Madras Presidency in the next 24 years.
His two appearances in Test matches came in England in 1936 when he was already 40. He wrote later in his autobiography that he was picked for non-cricketing reasons. Though well past his prime at the time, he scored 40 and 60 on debut and ended his career with an average of 56. He was a left-handed batsman and an attacking player. Ramaswami played for Hindus against Arthur Gilligan's MCC team in 1926-27 and scored 83 against Jack Ryder's Australian Services XI in 1935-36.
After the end of his career, he served as a selector, and manager to the Indian team to West Indies in 1952-53. His Ramblings of a Games Addict is one of the earliest autobiographies in Indian cricket. Ramaswami married Lakshmi Chaya Devi in 1928. He had two sons, Ram Swarup and Lakshman Swarup, and a daughter, Shantha Devi. Ram Swarup represented Madras and Andhra in first class cricket.
Ramaswami left his home in Adyar on the morning of 15 October 1985 and never returned. There have been occasional rumours about him being sighted. Wisden listed him as 'presumed dead' from 1988 to 1991. When doubts were raised about his fate, this was removed in 1992 but brought back in 1996. In the more recent editions, he has the status 'd. unknown'.