Integrated photonics has emerged as a pivotal technology in the advancement of next-generation computing and communication devices. Thermal optical phase shifters (OPSs) have been widely used to realize a tunable Mach-Zehnder interferometer (MZI) and a micro-ring resonator (MRR), which are the building bricks for the LSI/VLSI photonic integrated circuits. Due to the thermal crosstalk and the low modulation efficiency, thermal OPSs have large-scale size and high power consumption. In this work, we embed a Mie resonant metasurface into a waveguide and use the liquid crystal to tune the phase of the propagated light, which could realize a novel integrated phase shifter based on LC meta-waveguides. We use nanofabrication to prepare the meta-waveguide integrated MZI and MRR. By applying voltage, the output of the waveguide's intensity can be changed. Compared with thermo OPSs, this new modulator has the advantages of small size (20 μm × 0.35 μm), no thermal crosstalk, low power consumption (<
10 nW), and easy large-scale integration. Additionally, we apply it to the convolutional architecture and verify that it has the potential to accelerate neural network computation.