The ability to execute high-fidelity operations is crucial to scaling up quantum devices to large numbers of qubits. However, signal distortions originating from nonlinear components in the control lines can limit the performance of single-qubit gates. In this work, we use a measurement based on error amplification to characterize and correct the small single-qubit rotation errors originating from the nonlinear scaling of the qubit drive rate with the amplitude of the programmed pulse. With our hardware, and for a 15-ns pulse, the rotation angles deviate by up to several degrees from a linear model. Using purity benchmarking, we find that control errors reach 2×10-4, which accounts for half of the total gate error. Using cross-entropy benchmarking, we demonstrate arbitrary-angle single-qubit gates with coherence-limited errors of 2×10-4 and leakage below 6×10-5. While the exact magnitude of these errors is specific to our setup, the presented method is applicable to most sources of nonlinearity. Our work shows that the nonlinearity of qubit drive line components imposes a limit on the fidelity of single-qubit gates, independent of improvements in coherence times, circuit design, or leakage mitigation when not corrected for.