What is the dimension of Karuta cards?
Competition cards are 74x53mm (~2.9x2.1 inches) in size, and made from "pasteboard". Reference: Japanese Wikipedia article on karuta.  The pasteboard used to make Japanese playing cards tends to be thicker than what we are familiar with in the West for cards. It's called 厚紙 (atsugami = thick paper) and can be quite thick -- I have some Japanese playing cards that are 0.4mm thick, which is thicker than Western plastic playing cards, and I've seen images of atsugami that look quite a bit thicker.

Alas I don't know exactly how thick karuta competition cards are since I never held any.