Je suis droitier.
* Je suis means "I am"
* droitier means "right-handed"
You can also say:
Je suis gaucher.
This means "I am left-handed."
You can use this to clarify you're right-handed if the context is unclear. For example, you could say: "Je suis droitier, pas gaucher." This means "I am right-handed, not left-handed."