Carbon is emerging as a material with great potential for photovoltaics (PV). However, the amorphous form (a-C) has not been studied in detail as a PV material, even though it holds similarities with amorphous Silicon (a-Si) that is widely employed in efficient solar cells. In this work, we correlate the structure, bonding, stoichiometry, and hydrogen content of a-C with properties linked to PV performance such as the electronic structure and optical absorption. We employ first-principles molecular dynamics and density functional theory calculations to generate and analyze a set of a-C structures with a range of densities and hydrogen concentrations. We demonstrate that optical and electronic properties of interest in PV can be widely tuned by varying the density and hydrogen content. For example, sunlight absorption in a-C films can significantly exceed that of a same thickness of a-Si for a range of densities and H contents in a-C. Our results highlight promising features of a-C as the active layer material of thin-film solar cells.