You can use the event.ctrlKey flag to see if the Ctrl key is pressed. Something like this:

$( #textareaId ).keydown(function (e) {

  if (e.ctrlKey && e.keyCode == 13) {
    // Ctrl + Enter pressed
  }
});

Check the above snippet here.

Actually this one does the trick and works in all browsers:

if ((event.keyCode == 10 || event.keyCode == 13) && event.ctrlKey)

Link to js fiddle.

Notes:

• In Chrome on Windows and Linux, Enter would be registered as keyCode 10, not 13 (bug report). So we need to check for either.
• ctrlKey is control on Windows, Linux and macOS (not command). See also metaKey.

Universal solution

This supports macOS as well: both Ctrl+Enter and ⌘ Command+Enter will be accepted.

if ((e.ctrlKey || e.metaKey) && (e.keyCode == 13 || e.keyCode == 10)) {
    // do something
}

I found answers of others either incomplete or not cross-browser compatible.

This code works in Google Chrome.

$(function ()
{
    $(document).on("keydown", "#textareaId", function(e)
    {
        if ((e.keyCode == 10 || e.keyCode == 13) && e.ctrlKey)
        {
            alert( Ctrl + Enter );
        }
    });
});

This can be extended to a simple, but flexible, jQuery plugin as in:

$.fn.enterKey = function (fnc, mod) {
    return this.each(function () {
        $(this).keypress(function (ev) {
            var keycode = (ev.keyCode ? ev.keyCode : ev.which);
            if ((keycode ==  13  || keycode ==  10 ) && (!mod || ev[mod +  Key ])) {
                fnc.call(this, ev);
            }
        })
    })
}

Thus

$( textarea ).enterKey(function() {$(this).closest( form ).submit(); },  ctrl )

should submit a form when the user presses Ctrl + Enter with focus on that form s textarea.

(With thanks to How can I detect pressing Enter on the keyboard using jQuery?)

event.keyCode and event.which are deprecated.

The following works to handle CTRL/Command + Enter on Mac and Windows (React)

import React from "react";

export const Component = () => {
    const keyDownHandler = (e: React.KeyboardEvent<HTMLTextAreaElement>) => {
        if ((e.ctrlKey || e.metaKey) && e.key == "Enter") {
            // handle Ctrl/Command + Enter
        }
    };
    
    return (
        <textarea onKeyDown={keyDownHandler} />
    );
};

$( my_text_area ).focus(function{ set_focus_flag });

//ctrl on key down set flag

//enter on key down = check focus flag, check ctrl flag

Maybe a little late to the game, but here is what I use. It will also force submit of the form that is the current target of the cursor.

$(document.body).keypress(function (e) {
    var $el = $(e.target);
    if (e.ctrlKey && e.keyCode == 10) {
        $el.parents( form ).submit();
    } else if (e.ctrlKey && e.keyCode == 13) {
        $el.parents( form ).submit();
    }
});

First you have to set a flag when Ctrl is pressed; do this onkeydown.

Then you have to check the keydown of Enter. Unset the flag when you see a keyup for Ctrl.