If your file is similar to one already at the destination you could use rsync with the --fuzzy option. Fuzzy will look for a similarly named file in the destination directory and use it as the starting point for the copy sending only the differences between the two files across the wire.
As an example, here I'm copying xwiki-enterprise-web-3.4.war into a remote directory which already contains a xwiki-enterprise-web-3.2.1.war.
$ rsync -av --fuzzy xwiki-enterprise-web-3.4.war example.com:Downloads/xwiki-enterprise-web-3.4.war
sent 69065310 bytes received 74176 bytes 389518.23 bytes/sec
total size is 138567168 speedup is 2.00
You'll notice only about 1/2 the contents of the file actually needed transfer. It would be even better if the files were more similar as in this specific case the newer version xwiki is actually 26M larger than the older copy.
$ du -sh xwiki-enterprise-web-3.*