CRISPR-Cas9 is widely applied for genome engineering in various organisms. The assembly of single guide RNA (sgRNA) with the Cas9 protein may limit the Cas9/sgRNA effector complex function. We developed a FRET-based assay for detection of CRISPR-Cas9 complex binding to its targets and used this assay to investigate the kinetics of Cas9 assembly with a set of structurally distinct sgRNAs. We find that Cas9 and isolated sgRNAs form the effector complex efficiently and rapidly. Yet, the assembly process is sensitive to the presence of moderate concentrations of non-specific RNA competitors, which considerably delay the Cas9/sgRNA complex formation, while not significantly affecting already formed complexes. This observation suggests that the rate of sgRNA loading into Cas9 in cells can be determined by competition between sgRNA and intracellular RNA molecules for the binding to Cas9. Non-specific RNAs exerted particularly large inhibitory effects on formation of Cas9 complexes with sgRNAs bearing shortened 3′-terminal segments. This result implies that the 3′-terminal segment confers sgRNA the ability to withstand competition from non-specific RNA and at least in part may explain the fact that use of sgRNAs truncated for the 3′-terminal stem loops leads to reduced activity during genomic editing.