Optomechanical interaction in microstructures plays a more and more important role in the fields of quantum technology, information processing, and sensing, among others. It is still a challenge to obtain a strong optomechanical interaction in a compact device. Here, we propose and demonstrate that compact ring resonators consisting of silicon nanorods can realize strong optomechanical interaction even surpassing that of most optical microcavities. The proposed ring resonators can well confine infrared optical waves by the quasi-bound states in the continuum. Meanwhile, each nanorod in the resonator acts as a mechanical resonator of GHz resonating frequency, thus realizing an optomechanical coupling rate of up to 1.8 MHz. We have found that the interaction area can be extended by increasing the number of nanorods while maintaining the optomechanical interaction strength. Finally, we have studied the influence of supporting structures for suspended nanorods on the optomechanical interaction properties. The proposed ring resonators of silicon nanorods offer a promising platform for the study of optomechanical interaction.