$WINDOWID might be what you're looking for.
Note that whatever you do, it'll probably be an ugly hack that just happens to work with your favorite terminal at a hardcoded font size. E.g. how would your X app figure out the terminal's font size?
Also, keep in mind that there are terminals that have multiple tabs and your one might not be the visible one (e.g. gnome-terminal -- also beware that it's known in gnome-terminal that if you drag-n-drop a tab to another gnome-terminal window then $WINDOWID becomes incorrect because it can't be updated); there are terminals with split screen feature (e.g. gnome terminator) and then how do you figure out the offset; etc...