Ayr is a city in Cass County, North Dakota, United States. The population was 11 at the 2020 census. Ayr was founded in 1883. According to th…Ayr is a city in Cass County, North Dakota, United States. The population was 11 at the 2020 census. Ayr was founded in 1883. According to the United States Census Bureau, the city has a total area of 0.09 square miles, all land.