It is possible to run a bitcoin client which only connects to onion nodes in the TOR network, like that:
./bitcoind -onion=127.0.0.1:9050 -onlynet=tor -externalip=ssapp53tmftyjmjb.onion
Is something similar available for Ethereum?
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The answer is no, however Ethereum have developer The Whisper Protocol https://github.com/ethereum/wiki/wiki/Whisper have a read through, you may find it helpful in the absence of Tor availability.