Sexual abuse of a child is not only a crime that can (and should) result in criminal charges against the abuser. It is also wrongful conduct that makes the abuser liable for damages in a civil lawsuit.
Civil wrongs are called "torts." There are lots of categories of torts, but the two most applicable to sex abuse claims to minors are the tort of "battery" (the unlawful touching of another person) and "intentional infliction of emotional distress" (engaging in outrageous conduct that results in severe emotional injury to another). A person who commits a tort is liable for compensatory damages to the person injured by the conduct. If the tort is an intentional tort, or one that involves reckless conduct, the wrongdoer is also liable for punitive damages.
So, a child who is a victim of sexual abuse can (with the assistance of his or her parents or guardian) file a lawsuit against the abuser and seek compensatory and punitive damages for the injuries he or she suffered at the hands of the abuser. Whether the conduct occurred, what injuries were caused by the conduct, and the amount of damages to be awarded are issues that will be determined in the case.