If you need to remain anonymous that your even using Bitcoin I guess you have no choice but to download the whole blockchain through Tor. Otherwise you could download the whole chain normally then connect to Tor and then send your payments you want to send through Tor.
To keep anonymity while downloading, install Bitcoin, download the blockchain, and then copy over blkindex.dat and blk0001.dat to your anonymous system. Install the Bitcoin client there, and before starting it, copy the files to it's data directory.
the files blkindex.dat and blk0001.dat should be the same across all bitcoin installations. just the rest of the datadir and ofcourseyour wallet will make you identifiable.