We demonstrate optical tuning of the scattering length in a Bose-Einstein condensate as predicted by Fedichev {em et al.} [Phys. Rev. Lett. {bf 77}, 2913 (1996)]. In our experiment atoms in a $^{87}$Rb condensate are exposed to laser light which is tuned close to the transition frequency to an excited molecular state. By controlling the power and detuning of the laser beam we can change the atomic scattering length over a wide range. In view of laser-driven atomic losses we use Bragg spectroscopy as a fast method to measure the scattering length of the atoms.