Top-k selection algorithms are fundamental in a wide range of applications, including high-performance computing, information retrieval, big data processing, and neural network model training. In this paper, we present RTop-K, a highly efficient parallel row-wise top-k selection algorithm specifically designed for GPUs. RTop-K leverages a binary search-based approach to optimize row-wise top-k selection, providing a scalable and accelerated solution. We conduct a detailed analysis of early stopping in our algorithm, showing that it effectively maintains the testing accuracy of neural network models while substantially improving performance. Our GPU implementation of RTop-K demonstrates superior performance over state-of-the-art row-wise top-k GPU implementations, achieving an average speed-up of up to 11.49$\times$ with early stopping and 7.29$\times$ without early stopping. Moreover, RTop-K accelerates the overall training workflow of MaxK-GNNs, delivering speed-ups ranging from 11.97% to 33.29% across different models and datasets.