No reason why not, Ive done it off and on for years. The contaminates within the cardboard, i.e. ink and glue are minimal in the grand scale of things and should have no adverse effect on the final product, providing you do mix it up with plenty of other compostable material.

You'll find it composts better if you take smaller bits, scrunch them up and mix with green stuff.

This website explains how to make compost, and the mix of "greens" and "browns" you need.
http://www.recyclenow.com/home_composting/making_compost/index.html

Cardboard counts as "brown" no matter what's printed on it.