Graphene which is a single atom layer of carbon film with the interesting properties of high carrier mobility, high carrier concentration, high thermal conductivity, high velocity saturation, and reduced short channel effects, is emerging as a replacement of the ubiquitous silicon. This is particularly true for high-speed analog and radio-frequency electronics due to low $I_{on}/I_{off}$ ratio. In this paper, design exploration of a graphene FET (GFET) based $LC$-VCO is performed with wireless (WLAN) as the target application. Verilog-A based GFET modeling is performed. The model is used in design simulation, characterization, and sensitivity analysis of a cross-coupled version of an $LC$-VCO. In order to analyze the effects of nanoscale process variations, statistical process variation analysis of the GFET based $LC$-VCO is performed for selected figures of merit through exhaustive Monte Carlo simulations.