Delivery of self-amplifying mRNA (SAM) has high potential for infectious disease vaccination due its self-adjuvating and dose-sparing properties. Yet a challenge is the susceptibility of SAM to degradation and the need for SAM to reach the cytosol fully intact to enable self-amplification. Lipid nanoparticles have been successfully deployed at incredible speed for mRNA vaccination, but aspects such as cold storage, manufacturing, efficiency of delivery, and the therapeutic window would benefit from further improvement. To investigate alternatives to lipid nanoparticles, we developed a class of >200 biodegradable end-capped lipophilic poly(beta-amino ester)s (PBAEs) that enable efficient delivery of SAM and as assessed by measuring expression of SAM encoding reporter proteins. We evaluated the ability of these polymers to deliver SAM intramuscularly in mice, and identified a polymer-based formulation that yielded up to 37-fold higher intramuscular (IM) expression of SAM compared to injected naked SAM. Using the same nanoparticle formulation to deliver a SAM encoding rabies virus glycoprotein, the vaccine elicited superior immunogenicity compared to naked SAM delivery, leading to seroconversion in mice at low RNA injection doses. These biodegradable nanomaterials may be useful in the development of next-generation RNA vaccines for infectious diseases.