This report presents a low-power time integrator and its applications in an all-digital first-order ΔΣ time-to-digital converter (TDC). Time-to-Digital Converter (TDC) that map a time variable to a digital code is the most important building blocks of time-mode circuits. The time integrator is realized using a bi-directional gated delay line (BD-GDL) with time variable to be integrated as the gating signal. The integration of the time variable is obtained via the accumulation of the charge of the load capacitor and the logic state of gated delay stages. Issues affecting the performance of the time integrator and TDC are examined. The all-digital first-order ΔΣ TDC utilizing the time integrator was designed in using IBM 130 nm 1.2 V CMOS technology and analysed using Spectre ASP from Cadence Design Systems with BSIM4 models. A sinusoid time input of 333 ps amplitude and 231 kHz frequency with an oversampling ratio 68 was digitized by the modulator. The TDC provides first-order noise-shaping and a SNR of 34.64 dB over the signal band 48.27 ~ 231 kHz while consuming 293.8 μW.