Use native HTML5 Drag'n'Drop for text.

lib/ace/css/editor.css

@@ -5,6 +5,9 @@
     font-size: 12px;
     line-height: normal;
     color: black;
+    -moz-user-select: none;
+    -webkit-user-select: none;
+    user-select: none;
 }
 
 .ace_scroller {
@@ -23,6 +26,14 @@
     cursor: text;
 }
 
+.ace_content[draggable="true"] {
+    cursor: default;
+}
+
+.ace_selecting, .ace_selecting .ace_gutter{
+    cursor: text;
+}
+
 .ace_gutter {
     position: absolute;
     overflow : hidden;
@@ -258,10 +269,6 @@
     background-position: center center, top left;
 }
 
-.ace_editor.ace_dragging .ace_content {
-    cursor: move;
-}
-
 .ace_gutter-tooltip {
     background-color: #FFF;
     background-image: -webkit-linear-gradient(top, transparent, rgba(0, 0, 0, 0.1));