A car pulling to one side upon acceleration can be caused by several different things such as uneven tire pressure as in one tire could have more air than the other.
Or your tires could be out of balance or you have a tie rod problem or a steering linkage problem.
Another cause of a car pulling to one side when accelerating could be a bad wheel bearing or bad CV axle or something else wrong with the steering.
A bad brake caliper can also cause a car to pull to one side when accelerating if the brake caliper does not release properly.
Or you could have a slow leak in a brake line causing the car to pull to one side.
Either way if the car continues to pull to one side when accelerating it can lead to a dangerous situation and could cause you to lose control of the vehicle.
I would highly recommend taking the car to a mechanic if possible and have them check the steering and alignment and let them know that the car pulls to one side when you accelerate.