Born in 1991 in Maryland, Swaminathan grew up in a musical family with a mother who sang and a father who played the mridangam. Along with her sister, violinist Anjna Swaminathan, Rajna was encouraged to play music and first became interested in the mridangam around age five. However, as her fingers weren't strong enough initially to play the instrument, she also took piano lessons throughout her school years. She eventually began mentoring with veteran mridangam artist Umayalpuram K. Sivaraman, traveling to India over holidays to further her studies. Swaminathan also studied Carnatic vocal music and Bharatanatyam dancing. After high school, she earned degrees in anthropology and French from the University of Maryland, College Park. She also gained valuable performance experience working with the Ragamala Dance Company. It was during this period, in 2008, that she recorded the indian classical album The Sixth Element.
In 2012, Swaminathan won a research grant to play and study jazz in New York City. That put her in touch with a bevy of like-minded performers including pianist Vijay Iyer, saxophonist Steve Coleman, and trumpeter Amir ElSaffar, with whom she has continued to work. She also collaborated with playwright/actress Anu Yadav on scoring the music for her solo show Meena's Dream, issued in 2015 as The Worry Machine. Away from performing, Swaminathan holds workshops on the South Indian rhythmic perspective, and has done so at the Banff International Workshop in Jazz and Creative Music and at the Percussive Arts Society International Convention. She has also continued her studies, pursuing a PhD in music at Harvard University. In 2019, she released Of Agency and Abstraction, which featured her RAJAS ensemble with her sister, as well as guitarist Miles Okazaki, bassist Stephan Crump, saxophonist María Grand, and guest artists ElSaffar and vocalist Ganavya Doraiswamy. ~ Matt Collar, Rovi