The identification of structural variations (SVs) and viral integrations in circulating tumor DNA (ctDNA) is a key step in precision oncology that may assist clinicians in treatment selection and monitoring. However, due to the short fragment size of ctDNA, it is challenging to accurately detect low-frequency SVs or SVs involving complex junctions in ctDNA sequencing data. Here, we describe Aperture, a new fast SV caller that applies a unique strategy of $k$-mer-based searching, binary label-based breakpoint detection and candidate clustering to detect SVs and viral integrations with high sensitivity, especially when junctions span repetitive regions. Aperture also employs a barcode-based filter to ensure specificity. Compared with existing methods, Aperture exhibits superior sensitivity and specificity in simulated, reference and real data tests, especially at low dilutions. Additionally, Aperture is able to predict sites of viral integration and identify complex SVs involving novel insertions and repetitive sequences in real patient data. Aperture is freely available at https://github.com/liuhc8/Aperture.