Parker is a city in southeastern Fremont County, Idaho, United States. The population was 305 at the 2010 census. It is part of the Rexburg, Ida…Parker is a city in southeastern Fremont County, Idaho, United States. The population was 305 at the 2010 census. It is part of the Rexburg, Idaho Micropolitan Statistical Area. Parker is located at 43°57′31″N 111°45′33″W / 43.95861°N 111.75917°W.