A new accelerator dedicated to hadron therapy, the Heavy-Ion Therapy Facility in Lanzhou (HITFiL), is under construction. As the main accelerator of HITFiL, a heavy-ion synchrotron is designed with special attention paid to compact structure, high reliability and low cost. Stripping injection scheme is adopted for the synchrotron, which is more efficient than single-turn injection and less costly than multi-turn injection supported by electron-cooling. Carbon beams are adopted for HITFiL cancer therapy: C~(5+) ions from an electron cyclotron resonance ion source, are pre-accelerated by a cyclotron, stripped into C~(6+) ions by a carbon foil located in a main dipole of the ring and injected into the central orbit of the ring at the same time. The detailed injection scheme for the synchrotron is presented, and the stripping injection process is simulated. The injection efficiency, complete beam loss factors and the particle number gain are investigated. In addition, beam properties including beam distribution in real and phase space and emittance growth due to foil traversal are studied, and the required beam intensity is achieved.