Grannis is a city in Polk County, Arkansas, United States. The population was 554 at the 2010 census. Near Grannis is the Boggs Springs You…Grannis is a city in Polk County, Arkansas, United States. The population was 554 at the 2010 census. Near Grannis is the Boggs Springs Youth Encampment of the American Baptist Association, a retreat of Missionary Baptist churches.