The combination of Large Language Models (LLMs) and Federated Learning (FL) to leverage privacy-preserving data has emerged as a promising approach to further enhance the Parameter-Efficient Fine-Tuning (PEFT) capabilities of LLMs. In real-world FL settings with resource heterogeneity, the training process of Low-Rank Adaptation (LoRA), the representative PEFT method, still faces two major challenges: aggregagion noise and aggregagion misalignment. In this paper, we propose a novel Tensor-aggregated LoRA (Te-LoRA) in Federated Fine-tuning based on an alternating-freeze training strategy to avoid aggregating noise without additional server-side computational costs, while mitigating aggregation suboptimality caused by parameter misalignment between heterogeneous LoRAs. Especially in addressing the aggregation suboptimality issue, we design the Pre-Aggregation Alignment strategy (PAA-strategy) and Tensor-to-Matrix strategy (T2M-strategy) for aligning heterogeneous LoRAs and aggregating them into an united tensor, which is then decomposed into matrices adapted for client download. Extensive experiments demonstrate the effectiveness and robustness of Te-LoRA in both homogeneous and heterogeneous settings.