Yes, you can use GIT, but we can not help you since each router is different.
If your router does NAT, you need to figure out how to add a port mapping for the GIT port (213).
If your router has a firewall, you need to make sure that port is not blocked.
The way most NAT works is that you can make an outgoing connection, so you can be a GITclient and connect to a GITserver who is using tcp listen on port 213 and you do not need to make any changes. If you want to be the GITserver and listen on port 213 and you are behind NAT, you need to forward port 213 to the correct internet address that GIT is actually listening on.