(It looks like someone beat me to the punch with this answer while I was writing it! Sorry about that, I'll leave mine here for extra information!) There are a lot of dinosaur cartoons, but from your description you may be referring to the cartoon Dinosaur King which aired between 2007 to 2008, and focused on a trio of kids who each had their own pet dinosaur and called themselves the "D-Team." Each dinosaur had its own elemental attack, and could be summoned from and stored within a card using a special stone. The kids frequently faced off against a group of stranded time-traveling scientists. The D-Team try to protect their new dino friends from the scientists, and so it becomes a battle for who can collect the dinosaur cards first.

This also has some episodes on Youtube, including the first: