Integrated photonics enables signal synthesis, modulation and conversion using photonic integrated circuits (PICs). Many materials have been developed, among which silicon nitride (Si3N4) has emerged as a leading platform particularly for nonlinear photonics. Low-loss Si3N4 PICs have been widely used for frequency comb generation, narrow-linewidth lasers, microwave photonics and photonic computing networks. Yet, among all demonstrated functionalities for Si3N4 integrated photonics, optical non-reciprocal devices such as isolators and circulators have not been achieved. Conventionally, they are realized based on the Faraday effect of magneto-optic materials under an external magnetic field; however, it has been challenging to integrate magneto-optic materials that are not compatible with complementary metal–oxide–semiconductors and that require bulky external magnet. Here we demonstrate a magnetic-free optical isolator based on aluminium nitride (AlN) piezoelectric modulators monolithically integrated on low-loss Si3N4 PICs. The transmission reciprocity is broken by spatio-temporal modulation of a Si3N4 microring resonator with three AlN bulk acoustic wave resonators that are driven with a rotational phase. This design creates an effective rotating acoustic wave that allows indirect interband transition in only one direction among a pair of strongly coupled optical modes. A maximum of 10 dB isolation is achieved under 300 mW total radiofrequency power applied to three actuators, with minimum insertion loss of 0.1 dB. An isolation bandwidth of 700 MHz is obtained, determined by the optical resonance linewidth. The isolation remains constant over nearly 30 dB dynamic range of optical input power, showing excellent optical linearity. Our integrated, linear, magnetic-free, electrically driven optical isolator could be a key building block for integrated lasers and optical interfaces for superconducting circuits.