http://www.creativecrash.com/maya/script/gt-3-point-set-rotation Here's what you want. Pretty clever script, just run it, select the 3 verts that align to the rotation you want, and it'll set it. It's a little tedious but it gets you there.
I may be wrong but it's not as simple as you think due to Maya's internal rotation system thing. You'll need to rotate the object's axis to match the edge's orientation. Only viable way I can think of is by using script. Get the angle between 2 vertices, convert it to vector and transfer that to the object's axis rotation.…
I have these options in 2015. but I don't know the name for that tool options script to feed you the bits you need. :( Alternatively, you can get to the same function via marking menus for each tool, holding down w,e,r +lmb >Axis.