White light supercontinuum, which is generated by coupling short laser pulses into a nonlinear photonic crystal fiber, not only covers an extremely broad wavelength range (e.g., from visible to near infrared) but also has high spatial coherence. As a result, tightly focused supercontinuum can be used to trap a single particle and simultaneously to perform broad-band ultra-sensitive optical spectroscopy at a single particle level. In this paper we investigate the optical scattering spectroscopy of a single particle in white light supercontinuum optical tweezers. Lorenz-Mie theory and Fourier angular spectrum analysis are used to model the scattering of tightly focused supercontinuum by a uniform spherical scatterer. In addition, Born approximation method is applied to analyze scattering by non-spherical weak scatterers. Unlike conventional ensemble averaged spectroscopy, single particle spectroscopy has the unique capability to probe the properties of individual particles, which can lead to many important applications such as ultrasensitive sensing and nanoparticle characterization.