Fighting Cancer in Children Act This bill makes funding available for research and related activities concerning pediatric cancer that are conducted or supported by the National Institutes of Health (NIH) from funds previously made available to the NIH Office of the Director. Specifically, the bill transfers unobligated funding from the NIH Office of the Director and merges it with other NIH funding for biorepositories of pediatric cancer specimens and research on pediatric cancer survivorship. The bill also rescinds additional funding that was provided to the NIH Office of the Director.