If not for its inherently weak optical absorption at visible and infrared wavelengths, graphene would show exceptional promise for optoelectronic applications. Here we show that by nanopatterning a graphene layer into an array of closely packed graphene nanodisks, its absorption efficiency can be increased from less than 3% to 30% in the infrared region of the spectrum. We examine the dependence of the enhanced absorption on nanodisk size and interparticle spacing. By incorporating graphene nanodisk arrays into an active device, we demonstrate that this enhanced absorption efficiency is voltage-tunable, indicating strong potential for nanopatterned graphene as an active medium for infrared electro-optic devices.