As of the census of 2000, there were 3,012 people, 1,281 households, and 794 families residing in the town. The population density was 474.7/km² (1,227.1/mi²). There were 1,438 housing units at an average density of 226.6/km² (585.8/mi²). The racial makeup of the town was 80.54% White, 16.80% African American, 0.07% Native American, 0.37% Asian, 1.06% from other races, and 1.16% from two or more races. Hispanic or Latino of any race were 2.49% of the population.

There were 1,281 households out of which 27.9% had children under the age of 18 living with them, 40.8% were married couples living together, 17.7% had a female householder with no husband present, and 38.0% were non-families. 34.4% of all households were made up of individuals and 15.6% had someone living alone who was 65 years of age or older. The average household size was 2.26 and the average family size was 2.88.

In the town the population was spread out with 22.5% under the age of 18, 9.1% from 18 to 24, 26.6% from 25 to 44, 20.8% from 45 to 64, and 21.0% who were 65 years of age or older. The median age was 38 years. For every 100 females there were 82.8 males. For every 100 females age 18 and over, there were 78.0 males.

The median income for a household in the town was $26,364, and the median income for a family was $36,316. Males had a median income of $27,316 versus $19,706 for females. The per capita income for the town was $16,436. About 12.7% of families and 20.0% of the population were below the poverty line, including 26.5% of those under age 18 and 22.5% of those age 65 or over.

The most famous person from Pickens is Browning Bryant (January 24, 1957), who was a recording star in the late 1960s and early 1970s. On the strength of his record sales, he made numerous national TV appearances, including on Arthur Godfrey radio show, The Merv Griffin Show, The Mike Douglas Show (which he co-hosted for a week), The Ed Sullivan Show, The Tonight Show, and The Kraft Music Hall; he also performed in Las Vegas and did concerts around the U.S. Bryant, who still lives in Pickens, continues to write and record music. He is the only progeny of Maude and Ray Bryant.