If your child was born out of wedlock, the law says that he/she has to be legitimated under the law of the home country, or under the law of the father's residence or domicile (in or outside the United States), if such legitimation takes place before the child reaches the age of eighteen years and the child is in the legal custody of the legitimating parent or parents at the time of such legitimation, or on whose behalf a status, privilege, or benefit is sought by virtue of the relationship of the child to its natural mother or to its natural father if the father has or had a bona fide parent-child relationship with the person. Pretty long definition, and not easily readable, isn't it?
In any case, the answer is, yes, there is a way to bring your child, but it requires some paperwork. Consult an experienced immigration attorney.
If your name is not on your child's birth certificate, USCIS will require DNA evidence to establish your relationship. Depending on your citizenship status, your child may have derived U.S. citizenship from you at birth. Consult with an experienced immigration attorney for case specific advice.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation.
You will to establish that you are the parent - so regardless if you are the mother or father, you will need to start with DNA evidence.
If you are the father, were you married to the mother? If you were not, you will need to investigate the laws in the country where the child was born. US law requires that you establish paternity prior to the child's 18th birthday.
Once you have your evidence, you can then file your immigration petition,
Sign up to receive a 3-part series of useful information and advice about child custody law.