Yes, a bullet can be fired towards a fast moving car to puncture its tire. If you are asking this question with reference to the fact that the car is moving at a fast speed and it would not be possible to aim at its tire and for the bullet to hit it, it has to be kept in mind that a bullet fired from a gun travels at over 1000 m/s. The fastest land speed record is that of a jet-propelled car at 345 m/s. The general speed of car is around 30-40 m/s. If the car being fired at were truly moving at a very high speed, the gun can be aimed at a location where the car would reach by the time the bullet travels the distance.
In addition, the motion of the tire does not make a difference in the resistance of the tire to be pierced by a bullet. A general bullet can easily pass through a thin sheet of metal. The rubber that tires are made of would not present an obstacle to the motion of the bullet.