For fast processing of increasingly large graphs, triangle counting - a common building block of graph processing algorithms, is often performed on GPUs. However, applying massive parallelism to triangle counting is challenging due to the algorithm’s inherent irregular access patterns and workload imbalance. In this work, we propose WeTriC, a novel wedge-parallel triangle counting algorithm for GPUs, which, using fine(r)-grained parallelism through a lightweight static mapping of wedges to threads, improves load balancing and efficiency. Our theoretical analysis compares different parallelization granularities, while optimizations enhance caching, reduce work-per-intersection, and minimize overhead. Performance experiments indicate that WeTriC yields 5.63x and 4.69x speedup over optimized vertex-parallel and edge-parallel binary search triangle counting algorithms, respectively. Furthermore, we show that WeTriC consistently outperforms the state-of-the-art (i.e., on avg. 2.86x faster than Trust and 2.32x faster than GroupTC).