Capsid proteins in a subclass of RNA viruses each contains a flexible domain at the C or N terminus that is rich in positively charged amino acid residues (e.g. arginine) essential for genome packaging during viral replication. Electrostatic and other non-specific interactions between RNA and the end-grafted polypeptides determine the genome content and the nucleocapsid stability. Toward a quantitative understanding of the self-assembly process, we developed a coarse-grained model for the key components within the viral capsids and theoretically examined the effects of various non-specific intermolecular forces on the microscopic structure and the RNA length of the encapsidated genome. The theory predicts quantitative correlations of the genome size in a large number of wide-type RNA viruses with their capsid size, polypeptide chain length and charge density.