Lay down a 3 to 4 inch layer of compost mulch around the base of the grapevine. The layer should extend out 2 feet from the front and back of the vine.
Remove any plants near the grapes that are drawing mealybugs or aphids. These insects produce honeydew that attracts more ants. Removing the plants will deter the ant population from visiting the area.
Use a French plow to cultivate the soil between the vine rows, as recommended by the University of California Pest Management Program. This will keep down weeds that provide shelter to ants, and will also destroy any ant nests in the vineyard.
Set out ant traps in early spring and late summer. Use traps that contain grit baits for fire ants, and sugar-water baits for black ants.