As a rule, credit cards with high travel rewards are meant for users with higher creditworthiness. If you are planning to apply for any of the best travel rewards cards, your score should at least be described as "good," if not "excellent."
The exact credit history requirements may vary from card to card, however, options are limited for those in the lower 600s. Note that credit history is not the only factor that lenders will look at as they also normally consider your income and the amount of debt you have, among other things.