You can use the Jquery UI for drag and drop with an additional library that translates mouse events into touch which is what you need, the library I recommend is https://github.com/furf/jquery-ui-touch-punch, with this your drag and drop from Jquery UI should work on touch devises
or you can use this code which I am using, it also converts mouse events into touch and it works like magic.
function touchHandler(event) {
var touch = event.changedTouches[0];
var simulatedEvent = document.createEvent("MouseEvent");
simulatedEvent.initMouseEvent({
touchstart: "mousedown",
touchmove: "mousemove",
touchend: "mouseup"
}[event.type], true, true, window, 1,
touch.screenX, touch.screenY,
touch.clientX, touch.clientY, false,
false, false, false, 0, null);
touch.target.dispatchEvent(simulatedEvent);
event.preventDefault();
}
function init() {
document.addEventListener("touchstart", touchHandler, true);
document.addEventListener("touchmove", touchHandler, true);
document.addEventListener("touchend", touchHandler, true);
document.addEventListener("touchcancel", touchHandler, true);
}
And in your document.ready just call the init() function
code found from Here