There has been great interest in building compact synchrotrons for various applications, for example, inverse Compton scattering X-ray sources. However, the beam injection and extraction in compact rings require careful design for the lack of space. In this paper, we propose a simple combined injection-extraction scheme exploiting the fringe field of existing dipole magnets instead of additional septum magnets. This scheme is illustrated by using the 4.8 m ring proposed for Tsinghua Thomson scattering X-ray source as an example. Particle tracking is applied to demonstrate the validity of this scheme.