The hardware implementation of deep neural networks (DNNs) has recently received tremendous attention since many applications require high-speed operations. However, numerous processing elements and complex interconnections are usually required, leading to a large area occupation and a high power consumption. Stochastic computing has shown promising results for area-efficient hardware implementations, even though existing stochastic algorithms require long streams that exhibit long latency. In this paper, we propose an integer form of stochastic computation and introduce some elementary circuits. We then propose an efficient implementation of a DNN based on integral stochastic computing. The proposed architecture uses integer stochastic streams and a modified Finite State Machine-based tanh function to improve the performance and reduce the latency compared to existing stochastic architectures for DNN. The simulation results show the negligible performance loss of the proposed integer stochastic DNN for different network sizes compared to their floating point versions.