In addition to being an important object in theoretical and experimental studies in enzymology, RNase A also plays an important role in the development of many kinds of diseases by regulating various physiological or pathological processes, including cell growth, proliferation, differentiation, and invasion. Thus, it can be used as a useful biomarker for disease theranostics. Here, a simple, sensitive, and low-cost assay for RNase A was constructed by combining a fluorogenic substrate with reduced graphene oxide (rGO). The method with detection limit of 0.05 ng/mL was first applied for RNase A targeted drug screening, and 14 natural compounds were identified as activators of this enzyme. Then, it was applied to detect the effect of drug treatment and Hepatitis B virus (HBV) infection on RNase A activity. The results indicated that RNase A level in tumor cells was upregulated by G-10 and Chikusetsusaponin V in a concentration-dependent manner, while the average level of RNase A in the HBV infection group was significantly inhibited compared with that in the control group. Furthermore, the concentration-dependent inhibitory effect of heavy metal ions on RNase A was observed using the method and the results indicated that Ba2+, Co2+, Pb2+, As3+, and Cu2+ inhibited RNase A activity with IC50 values of 93.7 μM (Ba2+), 90.9 μM (Co2+), 110.6 μM (Pb2+), 171.5 μM (As3+), and 165.1 μM (Cu2+), respectively. In summary, considering the benefits of rapidity and high sensitivity, the method is practicable for RNase A assay in biosamples and natural compounds screening in vitro and in vivo.