Solid-state nanopores can be employed to detect and study local structure along single molecules by voltage driven translocation through the nanopore. Their sensitivity and versatility can be augmented by combining them with a direct force probe, for example, optical tweezers. Such a tool could potentially be used to directly probe RNA secondary structure through the sequential unfolding of duplex regions. Here, we demonstrate the first application of such a system to the study of RNA by directly measuring the net force on individual double-stranded RNA (dsRNA) molecules. We have probed the force on dsRNA over a large range of nanopore sizes from 35 nm down to 3.5 nm and find that it decreases as the pore size is increased, in accordance with numerical calculations. Furthermore, we find that the force is independent of the distance between the optical trap and the nanopore surface, permitting force measurement on quite short molecules. By comparison with dsDNA molecules trapped in the same nanopores, we find that the force on dsRNA is on the order of, but slightly lower than, that on dsDNA. With these measurements, we expand the possibilities of the nanopore-optical tweezers to the study of RNA molecules with potential applications to the detection of RNA-bound proteins, the determination of RNA secondary structure, and the processing of RNA by molecular motors.