In multi-task mixture-of-experts parameter-efficient fine-tuning, fixed-rank Low-Rank Adaptation (LoRA) adapters often struggle to accommodate the heterogeneous representation requirements across different tasks and network layers. Existing methods mainly focus on task-level expert selection, layer-wise rank allocation, or post-training parameter compression, making it difficult to jointly characterize low-rank capacity differences across tasks, layers, and modules within a unified framework. To address this issue, we propose Group-Sparse Routing-aware Low-Rank Adaptation (GSR-LoRA), a routing-aware structured rank compression method for multi-task parameter-efficient fine-tuning (PEFT). Specifically, we model low-rank components as selectable rank groups and use a task-dependent router to allocate rank capacity across tasks. Furthermore, we introduce a Group Lasso structured sparsity constraint to suppress redundant rank groups during training, forming a prunable adapter structure. During compression, we select rank groups by jointly considering parameter importance and routing usage signals, and map the router to the compressed rank space to obtain compact LoRA adapters that remain consistent with task routing. Experiments on GLUE show that GSR-LoRA reduces the average adapter rank from 16 to 5.5, removing 65.6% of rank components with only a 0.1-point performance degradation. These results demonstrate its ability to learn compact task-adaptive LoRA adapters while preserving multi-task performance. The code is available at https://github.com/HNLP93/GSR-LoRA