Lab-on-a-chip technology offers an ideal platform for low-cost, reliable, and easy-to-use diagnostics of key biomarkers needed for early screening of diseases and other health concerns. In this work, a graphene field-effect transistor (GFET) functionalized with target-binding aptamers is used as a biosensor for the detection of thrombin protein biomarker. Furthermore, this GFET is integrated with a microfluidic device for enhanced sensing performances in terms of detection limit, sensitivity, and continuous monitoring. Under this platform, a picomolar limit of detection was achieved for measuring thrombin; in our experiment measured as low as 2.6 pM. FTIR, Raman and UV-Vis spectroscopy measurements were performed to confirm the device functionalization steps. Based on the concentration-dependent calibration curve, a dissociation constant of KD = 375.8 pM was obtained. Continuous real-time measurements were also conducted under a constant gate voltage (VGS) to observe the transient response of the sensor when analyte was introduced to the device. The target selectivity of the sensor platform was evaluated and confirmed by challenging the GFET biosensor with various concentrations of lysozyme protein. The results suggest that this device technology has the potential to be used as a general diagnostic platform for measuring clinically relevant biomarkers for point-of-care applications.