Fairfax is a city in Linn County, Iowa, United States. The population was 2,828 at the time of the 2020 census. It is part of the Cedar Rapids M…Fairfax is a city in Linn County, Iowa, United States. The population was 2,828 at the time of the 2020 census. It is part of the Cedar Rapids Metropolitan Statistical Area. Fairfax was laid out in 1863 when the railroad was extended to that point. It was named after Fairfax County, Virginia.