Your setup is not super clear, but I will try to interpret. It sounds like you have a 24v ac signal connected to the coil on a relay. When that signal turns on, you want the relay to close. You want the arduino to use the relay contacts like a switch and detect whether it's open or closed.
I assume you mean that the contacts need some current? Assuming it's a mechanical relay, that's not really true. Some relays do recommend a bit of current to improve long term reliability, but I wouldn't worry about that right away.
Just hook up the contacts of the relay to your arduino as if it were a switch. Should work fine.
You could even hook up an LED to be turned on by the relay (google Led circuits). Set the current for 20ma, and that will give you a small load and a visual indicator at the same time.
If the relay is a solid state relay, it does need a load. But you haven't indicated that so I won't get into it.