The short answer is no. Basically, Tor is susceptible to timing correlation attacks, where someone who is observing the connection going from your client (OP) to the Tor network and also the connection from the Tor network to your destination can tell with fairly high certainty that they are the same connection.
Note that you would need to correlate data from multiple ISPs to do this. The traffic confirmation scenario, where I suspect that user X at ISP A is accessing site Y at ISP B, is fairly easy. The full deanonymization scenario would require me to analyze traffic from a large number of ISPs to look for correlations. As far as I know, there hasn't been an analysis of how easy this is to do at Internet scale, but there's no good reason to believe that it couldn't be done.
Note: For a timing attack to work they need to be able to single out just your traffic on Tor. If you run a full node on your computer and also use Tor to browse the Internet they cannot distinguish the traffic coming from you and for all the other routing taking place. This makes it impossible for them to do this with any reliability.