In my experience, even though it is an herb basil actually needs a "normal" amount of water. If the soil feels dry and the plant recovers when you water it, then it needs more water--either more frequent watering, or more thorough watering. When you apply water, soak the entire rootball--rather than just sprinkling the surface. (Be sure to allow excess water to drain away.) When the soil surface dries out, it's time to water again.
There are two other possibilities, however. One is that the plant is simply reacting to heat and perhaps wind and cannot take up water fast enough to make up for the speed at which it is transpiring. In this case it may wilt slightly even when it has been well watered. Providing it with a bit of shade at noon or during the afternoon will help if this is the case. Another possibility is that the roots have begun to fill the container, and it needs a larger pot with more soil.