The linking of antibiotic resistance gene with the plasmid vector became possible with:

The first recombinant DNA was constructed by Stanley Cohen and Herbert Boyer in 1972.
They cut a piece of DNA carrying an antibiotic resistance gene from a plasmid of Salmonella typhimurium using a restriction enzyme (the molecular scissors).
The cut piece of DNA was then linked with the plasmid DNA, which acted as the vector.
This linking of the antibiotic resistance gene with the plasmid vector became possible with the enzyme DNA ligase, which acts on cut DNA molecules and joins their ends by forming phosphodiester bonds.
Endonucleases cut DNA at specific sites within the molecule, exonucleases remove nucleotides from the ends, and DNA polymerase synthesises new DNA; none of these joins two DNA fragments.
So the enzyme is DNA ligase.