It's a custom logo. The script portion was designed in 1957, with the swash "C", and has undergone numerous tweaking. Prior to that "Cardinals" was spelled out in non-connecting letters.

You might find something similar enough for you at Mike Yanega's Script font ID guide:

http://bowfinprintworks.com/ScriptIDGuide.html

Don't think there's anything close enough here, but take a look:

http://www.fontshop.com/fontlist/genres/sports_script/

- Herb

Yes, Herb I should have looked closer at the dissimilar a's and said "lettering"!
Thanks for the links to script and sports fonts.