Well if Julia isn't scriptable as @khagler says, then you can usually use gui scripting. This will work as long as Julia has an edit menu and the keyboard shortcut for paste is cmd-v (like in most applications) and your cursor is placed in the proper location for the paste to work. Good luck.
tell application "TextWrangler"
set the_selection to (selection of front window as string)
if (the_selection) is "" then
set the_selection to line (get startLine of selection) of front window as string
end if
end tell
set the clipboard to the_selection
tell application "Julia-0.2.1" to activate
delay 0.2
tell application "System Events" to keystroke "v" using command down
EDIT: I see in your comments that a new Julia window opens every time the script is run. That might be happening because of the line... tell application "Julia" to activate. You might try this line of code in its place. It's another method to bring Julia frontmost before issuing the keystroke commands.
tell application "System Events" to tell process "Julia-0.2.1" to set frontmost to true
Note that if this doesn't bring the Julia window frontmost then it's because the process name is wrong. Sometimes the process name is different than the application name. If true you'll have to figure out the name of the Julia process which you can do by running this and finding its name. You may have to use "Terminal" if Julia runs in a Terminal window.
tell application "System Events" to return name of processes