Despite the tremendous development of oncology, prostate cancer remains a debilitating malignancy. One of the most promising approaches to addressing this issue is to exploit the advancements of nanomedicine in combination with well-established nuclear medicine and radiotherapy. Following this idea, we have developed a radioisotope nanocarrier platform of electron-beam-synthesized nanogels based on poly(acrylic acid). We have developed a functionalization protocol, showing the very high (>97%) efficiency of the conjugation in targeting a ligand–bombesin derivative. This engineered peptide can bind gastrin-releasing peptide receptors overexpressed in prostate cancer cells; moreover, it bears a radioisotope-chelating moiety. Our nanoplatform exhibits very promising performance in vitro; the radiolabeled nanocarriers maintained high radiochemical purity of >90% in both the labeling buffer and human serum for up to 14 days. The application of the targeted nanocarrier allowed also effective and specific uptake in PC-3 prostate cancer cells, up to almost 30% after 4 h, which is a statistically significant improvement in comparison to carrier-free radiolabeled peptides. Although our system requires further studies for more promising results in vivo, our study represents a vital advancement in radionanomedicine—one of many steps that will lead to effective therapy for castration-resistant prostate cancer.