www.m-w.com lists some interesting definitions for cardinal, including one which says that the bird is named after the ecclesiastical figure due to the color. My old dictionary at home lists as a definition the deep red color itself.

1 : a high ecclesiastical official of the Roman Catholic Church who ranks next below the pope and is appointed by him to assist him as a member of the college of cardinals
2 : CARDINAL NUMBER -- usually used in plural
3 : a woman's short hooded cloak orig. of scarlet cloth
4 [from its color, resembling that of the cardinal's robes] : a crested finch (Cardinalis cardinalis) of the eastern U.S. and adjacent Canada, the southwestern U.S., and Mexico to Belize which has a black face and heavy red bill in both sexes and is nearly completely red in the male


On a semi-related topic, I remain perplexed by the name of Stanford University's mascot, which is simply The Cardinal, in the singular, rather than the plural Cardinals of, say, the University of Louisville.