Cancio is both a given name and a surname. Notable people with the name include:
People with the given name Cancio Garcia (1937–2013), Filipino lawyer and jurist
People with the surname Hiram Rafael Cancio (1920–2008), American judge Hugo Cancio (born 1964), Cuban-born American businessman and political activist Leopoldo Cancio (1858–1927), Cuban politician and economist Raúl Cancio (1911–1961), Spanish actor