The Carolina Tartan was recognized as the official tartan of the state of South Carolina in 2002.

Tartan refers to fabric woven into plaid patterns representing clans (families) or regions in Scotland.

In old Scotland, the tartan was used for clothing and as a banner or flag. Because a family or community worked the cloth together, their clothing was made of the same patterns, and so a person could be recognized by the Tartan plaid that he wore. Tartans can also be designed as a symbol commemorating a special event or person.

From Tartans of Scotland:

"The Carolina tartan is based on a fragment of a coat of the Royal Company of Archers dated c.1730, believed to be the same sett as was used for the wedding ribbons of Charles II in 1661 - The tartan commemorates the historic link" (the Carolina colonies were named for Charles).

 
Quote from South Carolina legislation:

Whereas, Scottish families began to settle in both South and North Carolina during the last two decades of the seventeenth century; and

Whereas, in the first half of the eighteenth century, large numbers of both Highland Scots and Ulster Scots settled in the two Carolinas; and

Whereas, Scots became major elements of the population of both colonies; and

Whereas, a tartan is a plaid textile design consisting of stripes of varying width and color, each tartan unique to a clan, district, or group; and

Whereas, St. Andrew's Societies are organizations for the celebration of things Scottish; and

Whereas, St. Andrew's Societies in South and North Carolina arranged for the design of Carolina Tartan and cosponsored the effort for adoption of the design by the Scottish Tartans Society, which registered the Carolina Tartan in 1981, with the United Kingdom Design Registry; and

Whereas, those St. Andrew's Societies believe that the Carolina Tartan was the first one successfully advanced for a group of states in the United States, although Canadian provinces have had their distinctive tartans; and

Whereas, since 1981, tartans have been designed for other states; and

Whereas, the Carolina Tartan is a variation of a tartan associated with King Charles II who made the grant of land in 1663 which resulted in the creation of the Carolina proprietary colony; and

Whereas, there is desire on the part of many South Carolina citizens of Scottish descent to honor their ancestral ties. Now, therefore,

Be it enacted by the General Assembly of the State of South Carolina:

The Carolina Tartan is designated as the official tartan of the State of South Carolina.

The Scottish Tartans World Register also has a South Carolina Tartan:

Source:

Carolina Tartan: Tartans of Scotland
Carolina Tartan: The Scottish Tartans Museum
Scottish Tartans Museum; History
South Carolina Legislature Online

Links:

Cultural Symbols - 50 states