or: a website that tells you whether a given IP address was a Tor relay
Just because you see an Internet connection from a particular IP address does not mean you know who originated the traffic. Tor anonymizes Internet traffic by "onion routing," sending packets through a series of encrypted hops before they reach their destination. Therefore, if you see traffic from a Tor node, you may be seeing traffic that originated from someone using Tor, rather than from the node operator itself. The Tor Project and Tor node operators have no records of the traffic that passes over the network, but we do maintain current and historical records of which IP addresses are part of the Tor network.
ExoneraTor tells you whether there was a Tor relay running on a given IP address at a given time. ExoneraTor can further indicate whether this relay permitted exiting to a given server and/or TCP port. ExoneraTor learns these facts by parsing the public relay lists and relay descriptors that are collected from the Tor directory authorities and the exit lists collected by TorDNSEL. By inputting an IP address and time, you can determine whether that IP was then a part of the Tor network.
Notice: This service has moved to: https://exonerator.torproject.org/