Typically, the realization of strain vector sensing based on traditional optical fiber sensing is difficult. To address this, in this study, a multi-core optical fiber strain vector sensing system based on an in-phase and quadrature (IQ) modulated optical frequency domain reflector (OFDR) is designed and verified. The IQ modulation technique is used to perform a linear frequency sweep of the light source, and the strain vector information of a seven-core fiber after bending is obtained from the OFDR system using the spatial structure relation of multi-core fibers. Experimental results demonstrate that the spatial resolution of the bending strain is 28.35 cm in an 87 m seven-core fiber with a sweep frequency of 990 MHz. When the bending curvature of the optical fiber is 1.78 m^-1, the angular resolution is 29°. Moreover, the simulation analysis indicates that when the sweep frequency range increases to 10 GHz, a theoretical angular resolution of 1.02° can be achieved, which can further improve the system performance.