Convolutional neural networks (CNNs) are essential tools for computer vision tasks, but they lack traditionally desired properties of extracted features that could further improve model performance, e.g., rotational equivariance. Such properties are ubiquitous in biomedical images, which often lack explicit orientation. While current work largely relies on data augmentation or explicit modules to capture orientation information, this comes at the expense of increased training costs or ineffective approximations of the desired equivariance. To overcome these challenges, we propose a novel and efficient implementation of the Symmetric Rotation-Equivariant (SRE) Convolution (SRE-Conv) kernel, designed to learn rotation-invariant features while simultaneously compressing the model size. The SRE-Conv kernel can easily be incorporated into any CNN backbone. We validate the ability of a deep SRE-CNN to capture equivariance to rotation using the public MedMNISTv2 dataset (16 total tasks). SRE-Conv-CNN demonstrated improved rotated image classification performance accuracy on all 16 test datasets in both 2D and 3D images, all while increasing efficiency with fewer parameters and reduced memory footprint. The code is available at https://github.com/XYPB/SRE-Conv.