Because Jesus was also Jewish. The Old Testament is part of both Jewish and Christian tradition (and Muslim tradition too). In Christianity, the Old Testament points to the New Testament, it's not a separate thing at all. The first Christians were Jewish. The Jews were all waiting for the Messiah to come and save them. The Christians believe that Jesus was that messiah that was prophesied in the Old Testament, and therefore the Old Testament is an important part of the Christian tradition.