Neural networks have been widely used to analyze high-throughput microscopy images. However, the performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Highly relevant to the goal of automated cell phenotyping from microscopy image data is rotation invariance. Here we consider the application of two schemes for encoding rotation equivariance and invariance in a convolutional neural network, namely, the group-equivariant CNN (G-CNN), and a new architecture with simple, efficient conic convolution, for classifying microscopy images. We additionally integrate the 2D-discrete-Fourier transform (2D-DFT) as an effective means for encoding global rotational invariance. We call our new method the Conic Convolution and DFT Network (CFNet).