In the field of computer vision, face recognition has become a trending research topic, and is widely used in the area of network security. The transmission of data over a network via a cloud server exposes the information to security risks and privacy attacks, meaning that the use of an encryption algorithm is essential. Face recognition algorithms in robotics applications have become cumbersome in terms of the computation speed needed to recognize the image. Since this is a built-in programming function in the robotics board, it will limit the speed and security of data storage. To overcome this issue, a cloud server is utilized as this can improve the processing speed, throughput, efficiency, and robustness of face recognition. Storing images in the cloud server in a secure way requires that the image be encrypted. To achieve this, we propose a hybrid encryption technique based on bit slicing and a discrete Fourier transform (DFT), and develop a secure robotic face image recognition scheme using a MobileFaceNet-CNN model (BS-DFT-MobileFaceNet). The percentages of improvement in terms of accuracy over LeNet, VGG16Net, Alexnet, GoogLeNet, ResNet, MobileFaceNet including raw input image were 17.5%, 7.36%, 22.41%, 22.62%, 8.65%, and 288.89% for raw input images and encrypted images using Genetic Algorithm (GA), DNA Algorithm, Bit slicing, AES, DFT, and BS-DFT encryption algorithms respectively.