There's actually no technical reason why you couldn't do that with IP (4 or 6); although you'd need a approriately located host to be running a relay daemon[0].
0: ie something that takes, say, a UDP packet on port NNNN containing a whole raw IPv4 packet, throws away the wrapping, and drops the IPv4 packet onto its own network interface. This is safe - the packet must shrink by a dozen or two bytes with each retransmission - but usually not actually set up anywhere.
Edit: It probably wouldn't work for TCP though - maybe try TOR?