Backscatter Communication (BackCom) has been envisioned as a key enabler for ubiquitous connectivity in the Internet of Things (IoT). However, the inherent issues of limited range and low achievable bit rate are prominent barriers to the widespread deployment of BackCom. In this work, we address these challenges by considering a monostatic BackCom system assisted by an intelligent reflecting surface (IRS) and controlled seamlessly by data driven deep learning (DL) based approach. We propose a deep residual neural network (DRCNN) BackIRS-Net that exploits the unique coupling between the IRS phase shifts and the beamforming at the reader, to jointly optimize these quantities in order to maximize the effective signal to noise ratio (SNR) of the backscatter signal received at the reader. We show that the performance of a trained BackIRS-Net is close to the conventional optimization based approach while requiring much less computational complexity and time, which indicates the utility of this scheme for real-time deployment. Our results show that an IRS of moderate size can significantly improve backscatter SNR, resulting in range extension by a factor of 4 for monostatic BackCom, which is an important improvement in the context of BackCom based IoT systems.