The Edinburgh-based novelist tweeted a quote from US-born Angelou, a Grammy winner for her spoken word books, who died at home in Winston-Salem, North Carolina.
Rowling wrote: "If you are always trying to be normal, you will never know how amazing you can be. Maya Angelou" before adding her own touching tribute.
Dr Angelou was a prolific African-American author whose numerous awards including being honoured last year by America's National Book Awards for her service to the literary community.
Her groundbreaking autobiography I Know Why The Caged Bird Sings,a coming-of-age story in a hostile society in the American South in the 1930s and 1940s that deals with racism and rape, is a classic.
San Franciso's first black streetcar conductor [aged 16] published another book about her upbringing, Mom & Me & Mom, just last year.
"She was beyond simply being a writer of autobiography and poetry. I think she transcended the idea of writing and using writing as a transcendence medium to further the individual," Harold Augenbraum, executive director of The National Book Foundation said.
Dr Angelou was a Reynolds professor of US studies at Wake Forest University in Winston-Salum. A spokesman said: "Dr. Angelou was a national treasure whose life and teachings inspired millions around the world. including countless students, faculty, and staff."
Singer Cyndi Lauper tweeted: "She was a great light in the world."
Mary J Bilge's tribute included by quote by the professor that read: "There is no greater agony than bearing an untold story inside you."
Liberal Democrat MP Lynne Featherstone said she was "an incredible woman, writer and poet."
Dr Angelou, who has 411,000 followers on the micro-blogging site, poignantly tweeted six days ago: "Listen to yourself and in that quietude you might hear the voice of God."