The invention provides ligation reaction mixtures, methods, and kits for improved template-independent intramolecular ligation (circularization) of linear ssDNA, including denatured gDNA fragments or first-strand cDNA made by reverse transcription of RNA, using, for example, a thermostable RNA ligase. The circular ssDNA molecules obtained using the improved ligation reaction mixtures and methods can be used, for example, as templates: for amplification by inverse PCR, rolling circle replication, transcription, or for massively parallel DNA sequencing. Applications include, for example: gene expression analysis by qPCR or using microarrays; analysis of gDNA copy number variation; and detection or quantification of specific nucleic acid sequences for research, screening, medical diagnostics, theranostics, personalized medical treatment or breeding, for purposes such as human or animal medicine, forensics, or agriculture.