In the online manual, in the section on “Selecting and Dragging Lines”, it states:
To drag a single line, click the line number and (keeping the left mouse button depressed) drag it to the desired location.
I tried clicking and dragging a line up and then down per the instructions, and nothing happened. So I completely reset Komodo IDE by deleting my profile and restarting the program, but still it does not seem possible to click and drag a line.