What is the term used to describe the autonomously replicating circular extra-chromosomal DNA?

Plasmid.

The term used to describe the autonomously replicating circular extra-chromosomal DNA is "Plasmid." Plasmids are small, circular DNA molecules that exist independently of the chromosomal DNA in bacterial cells. They carry their own origin of replication, which allows them to replicate autonomously within the bacterial host. Plasmids can be used as vectors in genetic engineering to carry and transfer foreign DNA into host cells, making them valuable tools in recombinant DNA technology.

The construction of the first recombinant DNA emerged from the possibility of linking a gene encoding antibiotic resistance with a native plasmid (autonomously replicating circular extra-chromosomal DNA) of Salmonella typhimurium.

Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance.