Depends upon how you define the word; how historians have interpreted his times and actions; etc.   For a fact, he was elected a conservative Republican who used his positions to enact laws, ordinances, orders to limit monopolies; support unions; attack the worst of the Gilded Age; and usher in wider diversity.  He started with the Square Deal and ended with his 2012 New Nationalism.   http://www.pbs.org/tpt/slavery-by-another-name/themes/progressivism/

Most historians would place him as a progressive leader par excellence - recommend Doris Kearns Goodwin's The Bully Pulpit - http://www.nytimes.com/2013/11/12/books/bully-pulpit-doris-kearns-goodwins-book-on-roosevelt.html

These progressive programs led the way for Wilson's New Frontier, FDR's New Deal, Kennedy's New Frontier, and LBJ's Great Society.

Herbert Croly's "The Promise of America" should be required reading for all college degrees.