Non-reciprocal devices, such as circulators and isolators, are indispensable components in classical and quantum information processing in an integrated photonic circuit. Aside from those applications, the non-reciprocal phase shift is of fundamental interest for exploring exotic topological photonics, such as the realization of chiral edge states and topological protection. However, incorporating low optical-loss magnetic materials into a photonic chip is technically challenging. In this study, the non-reciprocal transmission in an optomechanical resonator is experimentally demonstrated for the first time. The underlying mechanism of the non-reciprocity demonstrated in this study is actually universal and can be generalized to any traveling wave resonators with a mechanical oscillator, such as the integrated disk-type microresonator coupled with a nanobeam. Considering that higher cooperativity and cascading of the optical devices have been reported in a photonic integrated chip, non-reciprocity in such an microresonator has applications for integrated photonic isolators and circulators, which will play important roles in a hybrid quantum Internet.