The apolipoprotein B mRNA-editing enzyme catalytic polypeptide-like 3 (APOBEC3) proteins are cell-encoded cytidine deaminases, some of which, such as APOBEC3G (A3G) and APOBEC3F (A3F), act as potent human immunodeficiency virus type-1 (HIV-1) restriction factors. These proteins require packaging into HIV-1 particles to exert their antiviral activities, but the molecular mechanism by which this occurs is incompletely understood. The nucleocapsid (NC) region of HIV-1 Gag is required for efficient incorporation of A3G and A3F, and the interaction between A3G and NC has previously been shown to be RNA-dependent. Here, we address this issue in detail by first determining which RNAs are able to bind to A3G and A3F in HV-1 infected cells, as well as in cell-free virions, using the unbiased individual-nucleotide resolution UV cross-linking and immunoprecipitation (iCLIP) method. We show that A3G and A3F bind many different types of RNA, including HIV-1 RNA, cellular mRNAs and small non-coding RNAs such as the Y or 7SL RNAs. Interestingly, A3G/F incorporation is unaffected when the levels of packaged HIV-1 genomic RNA (gRNA) and 7SL RNA are reduced, implying that these RNAs are not essential for efficient A3G/F packaging. Confirming earlier work, HIV-1 particles formed with Gag lacking the NC domain (Gag ΔNC) fail to encapsidate A3G/F. Here, we exploit this system by demonstrating that the addition of an assortment of heterologous RNA-binding proteins and domains to Gag ΔNC efficiently restored A3G/F packaging, indicating that A3G and A3F have the ability to engage multiple RNAs to ensure viral encapsidation. We propose that the rather indiscriminate RNA binding characteristics of A3G and A3F promote functionality by enabling recruitment into a wide range of retroviral particles whose packaged RNA genomes comprise divergent sequences.