We have employed high resolution angle resolved photoemission spectroscopy (ARPES) measurements to investigate many-body renormalizations of the single-particle excitations in $1T$-TiSe$_2$. The energy distribution curves of the ARPES data reveal intrinsic peak-dip-hump feature, while the electronic dispersion derived from the momentum distribution curves of the data highlights, for the first time, multiple kink structures. These are canonical signatures of a coupling between the electronic degrees of freedom and some Bosonic mode in the system. We demonstrate this using a model calculation of the single-particle spectral function at the presence of an electron-Boson coupling. From the self-energy analysis of our ARPES data, we discern some of the critical energy scales of the involved Bosonic mode, which are $sim$15 and 26 meV. Based on a comparison between these energies and the characteristic energy scales of our Raman scattering data, we identify these Bosonic modes as Raman active breathing (${text{A}}_text{1g}$) and shear (${text{E}}_text{g}$) modes, respectively. Direct observation of the band-renormalization due to electron-phonon coupling increases the possibility that electron-phonon interactions are central to the collective quantum states such as charge density wave (CDW) and superconductivity in the compounds based on $1T$-TiSe$_2$.
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