Press Ctrl + Shift + P on VS Code for the command menu and search for Julia Execute File. If you press enter then the command will be executed and the Julia file will be run.
You can also assign a key shortcut for the command: use again Ctrl + Shift + P and search for Preferences: Open Keyboard Shortcuts , then search again for Julia Execute File. I can’t remember what was originally assigned (or if any shortcut was assigned at all) but I set it to Ctrl + Shift + Enter (borrowed from Atom+Juno).