Anstis is a surname. Notable people with the surname include:
John Anstis (1669–1744), English officer of arms and antiquarian John Anstis, younger (1708–1754), Officer of arms at the College of Arms in London Marion Anstis, Australian herpetologist Stuart Anstis, guitarist and songwriter, former member of Cradle of Filth Thomas Anstis (died 1723), 18th-century pirate Toby Anstis (born 1968), British radio presenter
See also Anstice (disambiguation) Anstiss