A transient circularly polarized excitation and its implementation in a generalized dispersive material (GDM) model based discontinuous Galerkin time-domain (DGTD) solver are proposed for spectral analysis of chiral nanophotonic structures. The expression of a circularly polarized pulse with a certain bandwidth, which is real-valued and enables multi-physics and nonlinearity, is derived comprehensively. Numerical examples for nanophotonic structures, such as reflection of a metal mirror, transmission of an S-shaped dielectric metasurface, and chiroptical response of C4-symmetrically arranged right-handed enantiomers are presented to demonstrate the accuracy and capability of the proposed method.