A soccer ball curves when you kick it because the ball itself is spinning. By spinning, the ball unevenly deflects the air that’s traveling around it. To balance that deflected air, the soccer ball will experience a force that is perpendicular to the way it’s moving. It is this perpendicular force that pushes the ball to make it curve.

This phenomenon is generally called the Magnus Effect, and it shows up in other sports, too! A couple examples I can think of are putting topspin on a tennis serve, or pitching a curveball in baseball.

You will have to kick the soccer in the right way to make its orbit curve, in particular, you have to make it spin around its own center. When the soccer ball spins around its own center while moving forward in air, there is a "Bernoulli Equation" in hydrodynamics one can use to prove that, the air pressure on one side of the soccer is stronger than the other side, thus the soccer will curve to its side. Whether it curves to the left or right, depends on the direction of its spinning.