Final answer:
DNA ligase is the enzyme responsible for re-annealing the phosphate backbone of DNA segments after they have been cut by restriction enzymes during molecular cloning.
Step-by-step explanation:
The enzyme responsible for re-annealing the phosphate backbone of the DNA segments after a restriction digest is DNA ligase. This enzyme is crucial in the process of molecular cloning, as it facilitates the joining of DNA fragments by creating a covalent bond between the phosphate backbone and the deoxyribose sugar in DNA. This action is referred to as ligation, where DNA ligase 'glues' together the sticky ends produced by restriction enzymes during the cutting of DNA strands, allowing for the foreign DNA to be inserted into vectors such as plasmids.