Federated learning (FL) with differential privacy (DP) allows several organizations to learn a shared model from user data that only one organization is allowed to see. However, guaranteeing DP requires adding noise to gradients that scales with update dimensionality. While low-rank adaptation (LoRA) is a popular method for parameter-efficient fine-tuning, it is inherently sensitive to DP noise due to the multiplication operator. This noise amplification leads to significant utility degradation, hindering practical deployment in enterprise settings. To overcome this, we propose FedAnchor. Every round, FedAnchor captures compressed information using one of the LoRA matrices A and B, and then decompresses this to the complete adapted weight matrix via singular value decomposition (SVD) at the server. This relieves the model from DP noise exacerbation while maintaining full learning capacity. Experiments across multiple benchmarks demonstrate that FedAnchor matches the strongest baseline in non-private settings and outperforms it by 4.38% under stringent DP constraints (𝜖 = 3). At scale, FedAnchor maintains communication efficiency, computation robustness, and utility under strict privacy budgets, meeting the demands for enterprise-level cross-silo deployments.