My mom had made a fence aroung our back yard. Kids keep on trespassing by climbing on our fence. They do this because they want to cross from the apartments on the other side of our backyard to the street in front of our house. Can we call the police if this occures again?

Yes, calling the police is exactly what your mother should do.  In South Carolina, the trespasser(s) would face a fine up to $100 or up to 30 days in jail.  SC Code 16-11-600. 

There is another important factor to consider.  What happens if that trespasser gets injured while on your property? Would he or she be able to sue your mom? And would you be insured for the damages under your Homeowner's insurance policy? Many people worry about this and the danger of being sued is a big reason that many people put up fences.

In South Carolina, a trespasser who gets hurt on your property cannot sue you if you have permitted a dangerous condition to continue. In other states however, a trespasser may be able to sue the property owner. 

So, assuming that you live in South Carolina, your family cannot get sued by a trespasser as long as nobody intentionally hurt the trespasser.  Also, your family can call the police to have the trespassers arrested.  It may help if your mother put signs on the fence that would warn people that if they trespass, the police will get involved.