Parker is a city in Collin County, Texas, United States. The population was 5,462 in 2020. The first settlers arrived in the area that is now Parker i…Parker is a city in Collin County, Texas, United States. The population was 5,462 in 2020. The first settlers arrived in the area that is now Parker in the early 1840s. The town was named after William C. Parker, the son of the area's first known settler, John C. Parker. It was incorporated as a city on March 22, 1969.