In his career, he threw out a record 45.68% of all runners attempting to steal a base.
Ivan Rodriguez (I meant during the time of Ivan Rodriguez's career, he held the record, but due to the unclear wording of the question, I'll also accept Roy Campanella, who has the all-time caught stealing record of anyone's career, with a 57.40%) (edited at 8:09 am, July 18, 2017 (PDT))
Original Answer: Ivan Rodriguez