Yes you certainly can, see sshuttle (on the frontpage just now) for example. But you will not get transparent end-to-end connection (which hardly matters). Idea is to reconstruct something similar to kernel socket calls from actual TCP packets and send those calls to the other side (with retransmission handled only by outer reliable transport).
It's similar idea as "User"/"NAT-only"/"Outgoing only" networking option offered by various virtualization systems and emulators. Probably original historical implementation of this hack is slirp, which is unix tool that works as NATing SLIP endpoint without needing root access (or anything OS-specific), that was often used in early '90s to get "full" IP connectivity from UNIX account on internet-connected modem-accessible system (usually without official approval to do so).
It's similar idea as "User"/"NAT-only"/"Outgoing only" networking option offered by various virtualization systems and emulators. Probably original historical implementation of this hack is slirp, which is unix tool that works as NATing SLIP endpoint without needing root access (or anything OS-specific), that was often used in early '90s to get "full" IP connectivity from UNIX account on internet-connected modem-accessible system (usually without official approval to do so).