In this work we carried out density functional theory calculations combined with many-body perturbation formalism to study the structural, electronic and optical properties of a monolayer graphene sheet doped with Si. The electronic properties are analyzed at three levels of many-body GW approach (G0W0, GW0 and GW) constructed over a Generalized Gradient Approximation functional. By substituting carbon atoms by silicon atoms on graphene, the band gap of these materials can be continuously tuned by changing the concentration of Si. The optical properties and excitonic effects in these materials are investigated using the Bethe-Salpeter equation approach. The exciton energies show that these materials can absorb the visible light, and that the absolute positions of the excitonic peaks depend on the Si concentration. The optical absorption spectra of the Si-doped graphene are dominated by bound Frenkel exciton and the silicon doping increases the optical conductivity of graphene in the visible range. These materials may be applied in photonic and optoelectronic devices such as solar cells and light-emitters.