A service called Tweriod can do that. It takes a look at the people who follow you and, judging by their activity, gives you a graph that shows when they’re most likely to be online and reading.
After allowing Tweriod to access your Twitter account, you’re going to have a bit of a wait. Tweriod goes to work figuring out when your Twitter followers are most active, and will send you a DM when it has the information ready for your viewing.
The results? Simple, but impressive.