For this to work, you need to be building Julia from source, and you need to be using at least Julia version 0.3.
In your Julia base/ directory, create (or append to) a file called userimg.jl the line
require("Gtk")
Then build Julia as you normally would; the Gtk module will be available when julia starts.
In some cases, it might be necessary to add the path to the folder containing the Gtk shared libraries, for example:
push!(DL_LOAD_PATH, "/usr/lib/x86_64-linux_gnu")
require("Gtk")
pop!(DL_LOAD_PATH)
The "/usr/lib/x86_64-linux_gnu" needs to be replaced with the location of the GTK libraries on your system.
However, when the library is in a standard location -- such as /usr/lib, /usr/local/lib, or /usr/lib/x86_64-linux_gnu (on some systems) -- this step can be skipped.