Messenger RNA (mRNA) based vaccines have been introduced worldwide to combat the Covid-19 pandemic. These vaccines consist of non-amplifying mRNA formulated in lipid nanoparticles (LNPs). Consequently, LNPs are considered benchmark non-viral carriers for nucleic acid delivery. However, the formulation and manufacturing of these mRNA-LNP nanoparticles are expensive and time-consuming. Therefore, we used self-amplifying mRNA (saRNA) and synthesized novel polymers as alternative non-viral carrier platform to LNPs, which enable a simple, rapid, one-pot formulation of saRNA-polyplexes. Our novel polymer-based carrier platform consists of randomly concatenated ethylenimine and propylenimine comonomers, resulting in linear, poly(ethylenimine-ran-propylenimine) (L-PEI_x-ran-PPI_y) copolymers with controllable degrees of polymerization. Here we demonstrate in multiple cell lines, that our saRNA-polyplexes show comparable to higher in vitro saRNA transfection efficiencies and higher cell viabilities compared to formulations with Lipofectamine MessengerMAX™ (LFMM), a commercial, lipid-based carrier considered to be the in vitro gold standard carrier. This is especially true for our in vitro best performing saRNA-polyplexes with N/P 5, which are characterised with a size below 100 nm, a positive zeta potential, a near 100% encapsulation efficiency, a high retention capacity and the ability to protect the saRNA from degradation mediated by RNase A. Furthermore, an ex vivo hemolysis assay with pig red blood cells demonstrated that the saRNA-polyplexes exhibit negligible hemolytic activity. Finally, a bioluminescence-based in vivo study was performed over a 35-day period, and showed that the polymers result in a higher and prolonged bioluminescent signal compared to naked saRNA and L-PEI based polyplexes. Moreover, the polymers show different expression profiles compared to those of LNPs, with one of our new polymers (L-PPI₂₅₀) demonstrating a higher sustained expression for at least 35 days after injection.