In this paper, we demonstrate a vertical pin Ge-on-Si photo-detector on a wet-etched Si recess on a SOI wafer. A 120 nm-deep Si recess is etched on the SOI wafer with a 340 nm-thick top Si layer by the TMAH solution. The measured results show that the responsivity is more than 0.60 A/W for TE polarization and is more than 0.65 A/W for TM polarization at 1550 nm wavelength. Compared to the photo-detector without the Si recess, the responsivities for both TE and TM polarizations are improved by ~10%. A low dark current of 170 nA is achieved at a bias voltage of -1 V. And, the 3 dB-bandwidth at a bias voltage of -3 V is 21.5 GHz. This approach can be used to improve the coupling and absorption for high responsivity of photo-detector while maintain its high speed on a thick SOI platform based on the simulation results.