TERRY COUNTY, Texas—This remote swath of West Texas, dotted with bobbing oil-pump jacks and Angus steers, is never going to be confused with California’s Napa Valley or Bordeaux.

But among the rows of white-tufted cotton plants that have long been the area’s cash crop, farmers are increasingly cultivating a new product: wine grapes.

“I’m a West Texas boy who drinks beer,” said Brent Hogue, whose family is now growing Merlot and Albariño grapes alongside cotton. “With grapes we can hopefully survive in the farm.”

The Lone Star State now ranks as the nation’s fifth-largest wine producer, after California, Washington, New York and Oregon, according to Wines Vines Analytics, the research arm of trade publication Wines & Vines. Last year, Texas winemakers churned out 1.8 million cases, 36% more than in 2010.

The state’s industry generated $1.88 billion in economic activity in 2013, the most recent year available, a report by the Texas Wine and Grape Growers Association said last month.