Rawson was born in Providence, Rhode Island. His biological father was noted stage and film actor Richard Hart. His parents divorced shortly after he was born, and he was adopted by his stepfather, Jonathan Rawson.
Rawson's main discipline is as a theater critic. From 1983 to 2009, he was full-time theater critic and theater editor at the Pittsburgh Post-Gazette, covering theater not just in Pittsburgh but also irregularly in New York, London and the Canadian theater festivals. In 1984, he started the annual Post-Gazette (Pittsburgh) Performer of the Year Award, now (2017) in its 34th year. In 2009, he semi-retired, continuing as that paper's part-time senior theater critic. He also appears as the weekly critic for KDKA-TV. His B.A. is from Harvard University and his M.A. and Ph.D. from the University of Washington at Seattle.
Rawson is active in several theater organizations, including the editorial board of Best Plays, the standard theater yearbook established in 1920 by Burns Mantle. He is a board member of the American Theatre Hall of Fame, for which he helps supervise the annual nominations and balloting for the selection of new inductees. He has long been active in the American Theatre Critics Association, which he has twice served as chair (1991–93 and 2007–11) and for which he has organized conferences in London, at Connecticut's O'Neill Theater Center, at Canada's Shaw and Stratford Festivals and at the Oregon Shakespeare Festival; as of 2017, he continues to edit its website at www.americantheatrecritics.org.
Since 1968, Rawson has been a member of the English faculty at the University of Pittsburgh, where he has taught courses primarily in satire, Shakespeare, critical writing, Irish drama, and the work of playwright August Wilson, whom he came to know well through covering his plays since 1984 for the playwright's hometown newspaper of record. He is on the Board of Trustees (as secretary) of the Daisy Wilson Artist Community, named for Wilson's mother, which is restoring the August Wilson House at 1727 Bedford Ave. in Pittsburgh's Hill District, where Wilson lived his first 13 years and where his American Century Cycle of 10 plays can be said to have begun.
Since 2001 he has produced Off the Record, an annual musical theater satire of Pittsburgh news and newsmakers which raises funds for the Greater Pittsburgh Community Food Bank and other charities. In 1999, he wrote Where Stone Walls Meet the Sea, a 600-page centennial history of the Donald Ross-designed Sakonnet Golf Club in Little Compton, Rhode Island and of the summer colony of which it is a part. He and Laurence A. Glasco have written August Wilson: Pittsburgh Places in His Life and Plays (Pittsburgh History & Landmarks Foundation, 2nd edition, 2015) and their larger work, August Wilson's Pittsburgh, is expected in 2018, to be published by the University of Pittsburgh Press.