Embodiments are directed to methods for joining oligonucleotides. The methods include joining together one or more oligonucleotides by reacting an alkyne group linked to an oligonucleotide with an azide group linked to an oligonucleotide to form a triazole linkage. The alkyne group is a strained alkyne group. The methods can include ligating together ends of one or more oligonucleotides or cross-linking strands of an oligonucleotide duplex to form the triazole linkage. The methods described allow oligonucleotide strands to be ligated together without the need for a ligase enzyme. The methods can be useful for joining together single strands of DNA, cross-linking complementary strands, cyclizing single and double strands, labeling oligonucleotides with reporter groups, attaching DNA to surfaces, producing analogs of DNA with modified nucleobases and backbones, synthesizing large chemically modified RNA constructs, and creating biochemically active PCR templates.