Protein-based drugs are a promising class of therapeutics, but poor membrane permeability typically limits their application to extracellular receptors. Delivery strategies that can transport functional proteins to reach intracellular targets are needed, but with many current approaches, biomolecules become entrapped in the endosomes. This greatly reduces the effective concentrations of therapeutic agents at the target sites. Herein, we report a bioconjugation-based approach for intracellular protein delivery by site-selectively attaching amphiphilic polymers to the N-terminal positions of proteins using 2-pyridinecarboxaldehyde groups. The reaction is simple and features mild, aqueous conditions with no required genetic engineering of the proteins. Imaging studies demonstrate that the polymer-protein conjugates are successfully delivered into the cytosol of various cancer cell lines, likely through a membrane fusion mechanism. When conjugated to the delivery polymers, the activity of modified RNase A was retained and notably promoted cytotoxicity in cancer cells upon delivery to the cytosol. This work therefore provides a promising platform for protein-based material delivery for therapeutic applications.