River incision over geologic timescales can be a valuable indicator of regional surface uplift. However, extracting the timing of surface uplift relative to the onset of incision is complicated by changes in precipitation commensurate with topographic development. Evidence of large-scale river incision on the flanks of the Andean plateau has been cited in support of a rapid and recent surface uplift event. Recent climate modeling studies demonstrate large magnitudes of regional climate change associated with surface uplift of the Andes, which may have influenced river incision processes. Here we present an analysis of mid-Miocene (16 Ma) to present river incision of the southwest Peruvian Ocoña River. A Monte Carlo approach with ~1.6 × 105 different simulations is used to explore the range of surface uplift and paleoclimate histories that are compatible with the modern river profile and geological constraints on the incision timing and magnitude. A range of channel properties, including the erodibility coefficient and erosion threshold, are considered. Results indicate that deep canyon incision on the plateau flanks may not be as diagnostic of rapid surface uplift as previously thought. More specifically, the evolution of the Ocoña River is consistent with local plateau elevations of 1–3 km at 16 Ma and either a steady or punctuated uplift of 1.5–3.5 km since then. The range of acceptable uplift histories is sensitive to the long-term magnitude and temporal evolution of precipitation. Similar paleoprecipitation changes are expected to have modified river profile evolution elsewhere in the Andes.