Since VS 2013, the shortcut comes with built-in keybinds:
- AltUp
- AltDown
These move the selected line(s) up and down. If a line isn’t selected, but the text entry cursor is on the line, that also works without having to select the line.
If you wish to rebind it in Tools > Options > Environment > Keyboard, the identifier keys are Edit.MoveSelectedLinesUp and Edit.MoveSelectedLinesDown. You may need to remove your new combination from other existing keys first.