Nanoscale and power-efficient electro-optic (EO) modulators are essential components for optical interconnects that are beginning to replace electrical wiring for intra- and inter-chip communications. Silicon-based EO modulators show sufficient figures of merits regarding device footprint, speed, power consumption and modulation depth. However, the weak electro-optic effect of silicon still sets a technical bottleneck for these devices, motivating the development of modulators based on new materials. Graphene, a two-dimensional carbon allotrope, has emerged as an alternative active material for optoelectronic applications owing to its exceptional optical and electronic properties. Here, we demonstrate a high-speed graphene electro-optic modulator based on a graphene-boron nitride (BN) heterostructure integrated with a silicon photonic crystal nanocavity. Strongly enhanced light-matter interaction of graphene in a submicron cavity enables efficient electrical tuning of the cavity reflection. We observe a modulation depth of 3.2 dB and a cut-off frequency of 1.2 GHz.