Genetic introgression among closely related species is a widespread phenomenon across the Tree of Life and could be an important source of adaptive variation during early stages of diversification. In particular, genomic studies have revealed that many rapidly radiating clades tend to have complex, reticulate evolutionary histories. Although rapid radiations appear to be susceptible to introgression, they present special challenges for its detection because formal tests require accurate phylogenies, and paradoxically, introgression itself may obscure evolutionary relationships. To address this methodological challenge, we assessed introgression in a recent, rapid avian radiation in the Andes, the South American siskins (Spinus). Using ~45,000 SNPs, we estimated the Spinus phylogeny using multiple analytical approaches and recovered four strongly conflicting topologies. We performed a series of complimentary introgression tests that included valid tests for each of the likely species trees. From the consilience of test results, we inferred multiple introgression events among Andean Spinus in a way that was robust to phylogenetic uncertainty in the species tree. Positive tests for introgression were corroborated by independent population structure and ancestral assignment analyses, as well as a striking geographic pattern of mitochondrial haplotype sharing among species. The methodological approach we describe could be applied using any genomewide data, including SNP data, for clades without fully resolvable species trees. Our discovery of multiple introgression events within the Andean radiation of Spinus siskins is consistent with an emerging paradigm, that introgression tends to accompany the early stages of diversification.