The composer of the term 'I Got Rhythm' is George Gershwin, an American composer and pianist. He was born in Brooklyn, New York in 1898 and is considered one of the most important figures in American music. He wrote many popular songs, including 'Rhapsody in Blue' and 'An American in Paris', as well as the opera 'Porgy and Bess'. Gershwin's music combined elements of classical, jazz, and popular music, and he is remembered for his unique style and innovative approach to composition.