Interrogating plasma cell-free DNA (cfDNA) to detect cancer offers promise; however, no current tests scan structural variants (SVs) throughout the genome. Here, we report a simple molecular workflow to enrich a tumorigenic SV (DNA palindromes/fold-back inversions) that often demarcates genomic amplification and its feasibility for cancer detection by combining low-throughput next-generation sequencing with automated machine learning (Genome-wide Analysis of Palindrome Formation, GAPF-seq). Tumor DNA signal manifested as skewed chromosomal distributions of high-coverage 1-kb bins (HCBs), differentiating 39 matched breast tumor DNA from normal DNA with an average AUC of 0.9819. In a proof-of-concept liquid biopsy study, cfDNA from 0.5 mL plasma from prostate cancer patients was sufficient for binary classification against matched buffy coat DNA with an average AUC of 0.965. HCBs on the X chromosome emerged as a determinant feature and were associated with AR amplification. GAPF-seq could generate unique cancer-specific SV profiles in an agnostic liquid biopsy setting.