Final answer:
The enzyme that enables a transposon to move across the genome is transposase, which allows the transposon to excise from one location and integrate into another, introducing genetic diversity.
Step-by-step explanation:
The enzyme required for a transposon to move is transposase. Transposase catalyzes both the cut-and-paste and replicative transposition of Class II (DNA) transposons. This enzyme facilitates recombination between inverted repeats, excision of the transposon from its original location, and integration into a new location in the DNA. The action of transposase introduces genetic diversity as it allows the transposon to affect the phenotype of the cell by potentially inactivating or activating different genes.