Confusingly there are two terminal emulators out there called Terminator. One is a Java-based, the other is based on Gtk+ and is suited for the GNOME desktop (sometimes this one is also referred to as
gnome-terminator). Your link and the tag applied to the question contradicts as for which one you're referring to.
I'll be talking about "gnome-terminator" here, which you can easily recognize by the red header bar.
Terminator, as many other terminal emulators, uses the VTE widget for terminal emulation. Unfortunately, the latest tarball release (0.98 as of writing this) still uses GTK+ version 2, and its corresponding VTE version 0.28 which does not support rewrapping. Rewrapping was implemented in VTE version 0.36 which requires GTK+ v3.
There is a bazaar branch of Terminator that uses GTK+-3 and VTE 0.38 or newer. It's available at https://code.launchpad.net/~gnome-terminator/terminator/gtk3. If you download, compile and install it, you'll get rewrapping along with about a hundred other improvements and fixes.
In the mean time, could you please push the author to releasing a GTK+-3 version? You can do it e.g. at https://bugs.launchpad.net/terminator/+bug/1030562.
Note that Terminator's GTK+-3 branch is not fully release-ready yet, you might encounter a few minor glithces that don't exist in the GTK+-2 branch (see also the aforementioned bugreport for 3 patches that I recommend to apply), but it's in an overall very good state, it'll work pretty nicely.
Update: Terminator version 1.90 is out now based on GTK+-3 and corresponding VTE versions, and as such, supports rewrapping.