The objective of point cloud place recognition is to convert a point cloud into a global descriptor that can be utilized in autonomous driving applications to identify the best-matched road scene from an extensive dataset. However, capturing a point cloud from an arbitrary view by robots or self-driving vehicles often involves scene rotations, making existing deep learning-based methods susceptible to errors.To quantify this performance degradation, we introduce a novel metric: Average Recall@N under arbitrary rotations, denoted as ''R-AR@N''. To address this issue, we propose a Geometrical Transformation Module designed to convert rotation-sensitive coordinates into rotation-invariant representations. Additionally, we observe that the design of overly complex networks may not be crucial for effective point cloud analysis. In line with the straightforward architectural design of PointMLP \cite{pointmlp}, we introduce a Local Feature Transformation module that utilizes statistical representations to transform local point features within a reasonable range. This enables the network to capture diverse geometric structures and generate a robust global descriptor.Our proposed method undergoes extensive evaluation on the Oxford outdoor dataset and three in-house datasets, demonstrating an improvement of at least 2% over previous methods on the newly proposed ''R-AR@N'' metric. Our code is available at https://github.com/jasonwjw/RI-PointMLP