The peculiar properties of the gapless surface states with a Dirac cone shaped energy dispersion in topological insulators (TIs) enable promising applications in photodetection with an ultra-broad band and polarization sensitivity. Since many TIs can be easily grown on silicon (Si) substrates, TIs on Si could make an alternative route for photon detection of Si photonics. We present good device performances of a Si-based single-crystal bismuth telluride (Bi₂Te₃) photoconductive detector. Room temperature photo responses to 1064 nm and 1550 nm light illumination were demonstrated. Linear dependences of the photocurrent on both the incident light power and the bias voltage were observed. The main device parameters including responsivity and quantum efficiency were extracted.