Using density functional theory calculations, we demonstrate that the electronic and optical properties of a buckled arsenene monolayer can be tuned by molecular doping. Effective p-type doping of arsenene can be realized by adsorption of tetracyanoethylene and tetracyanoquinodimethane (TCNQ) molecules, while n-doped arsenene can be obtained by adsorption of tetrathiafulvalene molecules. Moreover, owing to the charge redistribution, a dipole moment is formed between each organic molecule and arsenene, and this dipole moment can significantly tune the work function of arsenene to values within a wide range of 3.99-5.57 eV. Adsorption of TCNQ molecules on pristine arsenene can significantly improve the latter's optical absorption in a broad (visible to near-infrared) spectral range. According to the AM 1.5 solar spectrum, two-fold enhancement is attained in the efficiency of solar-energy utilization, which can lead to great opportunities for the use of TCNQ-arsenene in renewable energy. Our work clearly demonstrates the key role of molecular doping in the application of arsenene in electronic and optoelectronic components, renewable energy, and laser protection.