The possibility of utilizing the rich spin-dependent properties of graphene has attracted much attention in the pursuit of spintronics advances. The promise of high-speed and low-energy-consumption devices motivates the search for layered structures that stabilize chiral spin textures such as topologically protected skyrmions. Here we demonstrate that chiral spin textures are induced at graphene/ferromagnetic metal interfaces. Graphene is a weak spin-orbit coupling material and is generally not expected to induce a sufficient Dzyaloshinskii-Moriya interaction to affect magnetic chirality. We demonstrate that indeed graphene does induce a type of Dzyaloshinskii-Moriya interaction due to the Rashba effect. First-principles calculations and experiments using spin-polarized electron microscopy show that this graphene-induced Dzyaloshinskii-Moriya interaction can have a similar magnitude to that at interfaces with heavy metals. This work paves a path towards two-dimensional-material-based spin-orbitronics.