Enzymes that degrade synthetic polymers have attracted intense interest for eco-friendly plastic recycling. However, because enzymes did not evolve for the cleavage of abiotic polymers, directed evolution strategies are needed to enhance activity for plastic degradation. Previous directed evolution efforts relied on polymer degradation assays that were limited to screening ∼104 mutants. Here, we report a high-throughput yeast surface display platform to rapidly evaluate >107 enzyme mutants for increased activity in cleaving synthetic polymers. In this platform, individual yeast cells display distinct mutants, and enzyme activity is detected by a change in fluorescence upon the cleavage of a synthetic probe resembling a polymer of interest. Highly active mutants are isolated by fluorescence activated cell sorting and identified through DNA sequencing. To demonstrate this platform, we performed directed evolution of a polyethylene terephthalate (PET)-depolymerizing enzyme, leaf and branch compost cutinase (LCC). We identified activity-boosting mutations that substantially increased the kinetics of degradation of solid PET films. Biochemical assays and molecular dynamics (MD) simulations of the most active variants suggest that the H218Y mutation improves the binding of the enzyme to PET. Overall, this evolution platform increases the screening throughput of polymer-degrading enzymes by 3 orders of magnitude and identifies mutations that enhance kinetics for depolymerizing solid substrates.