This new research from bit.ly diagrams when tweets with links get the most traffic/clicks (Times are EST). The darker the color, the more traffic on average links posted during that hour received:
INTERPRETATION: Posts between 1-3pm Monday-Thursday get the high click counts. So stick to afternoons earlier in the week to get the most traffic from your links.
However, Twitter is actually busier a little before these times, so posting earlier might get you more retweets, favs or visibility. This next chart works the same way, except that the darker the color of the square, the higher the total number of clicks on Bitly links coming from Twitter were overall: