Modern distributed systems generate massive volumes of log data that are critical for detecting anomalies and cyber threats. However, in real world settings, these logs are often distributed across multiple organizations and cannot be centralized due to privacy and security constraints. Existing log anomaly detection methods, including recent large language model (LLM) based approaches, largely rely on centralized training and are not suitable for such environments. In this paper, we propose DP-FLogTinyLLM, a privacy preserving federated framework for log anomaly detection using parameter efficient LLMs. Our approach enables collaborative learning without sharing raw log data by integrating federated optimization with differential privacy. To ensure scalability in resource constrained environments, we employ low rank adaptation (LoRA) for efficient fine tuning of Tiny LLMs at each client. Empirical results on the Thunderbird and BGL datasets show that the proposed framework matches the performance of centralized LLM based methods, while incurring additional computational overhead due to privacy mechanisms. Compared to existing federated baselines, DP-FLogTinyLLM consistently achieves higher precision and F1-score, with particularly strong gains on the Thunderbird dataset, highlighting its effectiveness in detecting anomalies while minimizing false positives.