Perfect Rhymes (same vowel and ending sound):
* There aren't any true perfect rhymes for "litigator" in common usage.
Near Rhymes (similar vowel sound but different ending):
* Elevator
* Negotiator
* Investigator
* Illustrator
Eye Rhymes (spelled similarly but pronounced differently):
* Iterator
Slant Rhymes (similar but not identical sounds):
* Operator
* Collaborator
* Facilitator
The best option really depends on the context of your rhyme.