He has been a board member since the early 1990s of the American Theatre Hall of Fame, for which, succeeding Henry Hewes (critic), he supervises the annual nominations and balloting for the selection of new inductees.
He has long been active in the American Theatre Critics Association (ATCA), 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.
For some years he was on the editorial board of Best Plays, the standard theater yearbook established in 1920 by Burns Mantle.
From 1968, and as Emeritus since 2018, Rawson was a member of the English faculty at the University of Pittsburgh, where he taught courses primarily in satire, Shakespeare, critical writing, Irish drama, and the work of playwright August Wilson.
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.