You mean instead of using the TCP stack included in the kernel, you want to write your own? You could use raw sockets (described in man 7 raw) for that (but note that they require elevated privilege). Use socket(PF_INET, SOCK_RAW, IPPROTO_TCP) to get a raw TCP socket, then send and receive TCP packets as raw bytes over the socket.

I found an example demonstrating the approach here: http://www.tenouk.com/Module43a.html