We demonstrate a 10Gb/s Graphene Phase Modulator (GPM) integrated in a Mach-Zehnder interferometer configuration. This is a compact device, with a phase-shifter length of only 300$mu$m, and 35dB extinction ratio. The GPM has modulation efficiency of 0.28Vcm, one order of magnitude higher compared to state-of-the-art depletion p-n junction Si phase modulators. Our GPM operates with 2V peak-to-peak driving voltage in a push-pull configuration, and it has been tested in a binary transmission of a non-return-to-zero data stream over 50km single mode fibre. This device is the key building block for graphene-based integrated photonics, enabling compact and energy efficient hybrid Si-graphene modulators for telecom, datacom and other applications