Odds of Getting In
There are a few paths you can take to become a corporate relocation specialist, and a few specializations that may help you get in. You certainly look more attractive to corporate HR departments if you have real estate, management (especially with a moving company), or prior human resources experience.
Starting your career in any of those areas will get your foot in the door. If you have your sights set on global relocation, realize it will take a while to get the necessary experience for such a position.
Then again, if you're a military brat (and we use the term with affection, of course), your life experience may qualify you much sooner than you think. Ironically, if you have your sights set on specifically becoming a relocation specialist, you may have to move to a city where your preferred position exists.