Graphics Processing Units (GPUs) are increasingly used to accelerate portions of general-purpose applications. Higher level language extensions have been proposed to help non-experts bridge the gap between a host and the GPU's threading model. Recent updates to the OpenMP standard allow a user to parallelize code on a GPU using the well known fork-join programming model for CPUs. Mapping this model to the architecturally visible threading model of typical GPUs has been challenging. In this work we propose a novel approach using the technique of Warp Specialization. We show how to specialize one warp (a unit of 32 GPU threads) to handle sequential code on a GPU. When this master warp reaches a user-specified parallel region, it awakens unused GPU warps to collectively execute the parallel code. Based on this method, we have implemented a Clang-based, OpenMP 4.5 compliant, open source compiler for GPUs. Our work achieves a 3.6x (and up to 32x) performance improvement over a baseline that does not exploit fork-join parallelism on an NVIDIA k40m GPU across a set of 25 kernels. Compared to state-of-the-art compilers (Clang-ykt, GCC-OpenMP, GCC-OpenACC) our work is 2.1 - 7.6x faster. Our proposed technique is simpler to implement, robust, and performant.