The Center for Disease Control lists the average height for an American woman as 63.8 inches, or 5 feet 3.8 inches. Wikipedia uses a similar figure, listing the average height of American women as 5 feet 4 inches.
The average height of American women has consistently increased since at least the 19th century. Until recently, both American men and American women were among the tallest people in the world. In recent years, Americans' height growth has been outpaced by western European countries; this has led to modern American men being ranked 9th tallest in the world and American women ranking in at 15th tallest.