We theoretically study the broadband near-field optical spectrum of twisted bilayer graphene (TBG) at various twist angles near the magic angle using two different models. The spectrum at low Fermi energy is characterized by a series of peaks that are almost at the same energies as the peaks in the far-field optical conductivity of TBG. When the Fermi energy is near a van Hove singularity, an additional strong peak appears at finite energy in the near-field spectrum, which has no counterpart in the optical conductivity. Based on a detailed calculation of the plasmon dispersion, we show that these spectroscopic features are associated with interband and intraband plasmons, which can provide critical information about the local band structure and plasmonic excitations in TBG. The near-field peaks evolve systematically with the twist angle, so they can serve as fingerprints for identifying the spatial dependent twist angle in TBG samples. Our findings pave the way for future experimental studies of the novel optical properties of TBG in the nanoscale.