The 26-year-old is a two-time Olympian, previously finishing seventh in the mixed team relay and 12th in the women’s competition in Beijing.
Farquharson went into Tuesday’s competition in fifth, leading for the U.S. women. After four runs over two days, Farquharson slid into third, earning Olympic bronze.
Latvia’s Elina Bota took silver and Germany’s Julia Taubitz won gold.
Farquharson got her start in luge through the Youth Sports Alliance’s after-school program when she was 11 years old.
She is the second member of the Park City Nation to earn a medal at this year’s Olympics. Earlier Tuesday, freeskier Alex Hall claimed silver in the men’s slopestyle.
The Park City Nation makes up about a fifth of the U.S. delegation at the Winter Games with more than 40 athletes representing the Wasatch Back town.