Basil requires proper soil and water management to thrive, and both dry soil and overwatering are among the most common causes for wilting basil leaves.
Insert your finger into the top inch of the soil, and if it’s dry, water your plant immediately. Make sure to avoid its leaves, and stop when the water begins to drain out of the pot.
To prevent wilting leaves from recurring, stay observant until you can establish an effective watering schedule for your plant's particular conditions.