you could spoof packets by creating a packet with and modifying the source IP address, however this would be pointless for anything connection oriented, i.e. using tcp since the server you connect to will not be able to establish a connection to you since it will be sending all acknowledgements to the spoofed IP address. For UDP or any other connectionless protocol this will work fine.
If it is for anonymous web browsing then try finding a proxy server, there are plenty of free ones, however ensure that it does mask your IP address since many are transparent and dont