In the construction industry, the construction process of rebar tying is highly dependent on manual operation, which leads to a wide range of work areas, high labor intensity, and limited efficiency. Therefore, robot technology for automatic rebar tying has become an inevitable trend in on-site construction. This study aims to develop a planar rebar-tying robot that can achieve autonomous navigation, precise positioning, and efficient tying on a plane rebar mesh without boundaries. Our research covers the overall design of the robot control systems, the selection of key hardware, the development of software platforms, and the optimization of core algorithms. Specifically, to address the technical challenges of accurately recognizing the tying position and status, we propose an innovative two-stage identification method that combines a depth camera and an industrial camera to obtain image information about the area to be tied. The effectiveness of the planar rebar-tying robot system, including the recognition method proposed in this study, was verified by experiments on a rebar mesh demonstration platform. The following application of our robot system in the field of the Shenyang Hunnan Science and Technology City Phase IV project achieved satisfactory performance. It is shown that this research has made a unique and significant innovation in the field of automatic rebar tying.