Hi saenny,
No, I do not think that this warrants getting tested. Hepatitis C needs to be blood-to-blood meaning that blood infected with Hepatitis C needs to get deep into your body. Papercuts can bleed a lot, but they are shallow cuts. Even if there were somehow live viral particles on the bill right on the very edge that cut you (highly doubtful), your cut had blood coming out of it, which would wash any of the Hepatitis C outside of your body, not suck it in.
In health care settings, doctors and nurses who accidentally stick themselves with a needle that has just been used on a patient that they know is Hepatitis C positive only are infected at a rate of 3% of the time - 97% of the time, nothing happens. What happened to you isn't even close to a needle stick, and you have no idea if some Hep C infected blood was even on the bill, so your odds of becoming infected are non-existent.
Money is contaminated with germs but getting a papercut from it might result in a topical bacterial infection, but that's about it. You are going to be fine and no need to get tested for Hepatitis C because of this papercut.