DNA G-quadruplex (G4) structures, either within gene promoter sequences or at telomeres, have been extensively investigated as potential small-molecule therapeutic targets. However, although G4s forming at the telomeric DNA have been extensively investigated as anticancer targets, few studies focus on the telomeric repeat-containing RNA (TERRA), transcribed from telomeres, as potential pharmacological targets. Here, a virtual screening approach to identify a library of drug-like putative TERRA G4 binders, in tandem with circular dichroism melting assay to study their TERRA G4-stabilizing properties, led to the identification of a new hit compound. The affinity of this compound for TERRA RNA and some DNA G4s was analyzed through several biophysical techniques and its biological activity investigated in terms of antiproliferative effect, DNA damage response (DDR) activation, and TERRA RNA expression in high vs. low TERRA-expressing human cancer cells. The selected hit showed good affinity for TERRA G4 and no binding to double-stranded DNA. In addition, biological assays showed that this compound is endowed with a preferential cytotoxic effect on high TERRA-expressing cells, where it induces a DDR at telomeres, probably by displacing TERRA from telomeres. Our studies demonstrate that the identification of TERRA G4-targeting drugs with potential pharmacological effects is achievable, shedding light on new perspectives aimed at discovering new anticancer agents targeting these G4 structures.