It probably could be done with some sort of script. Still, would not necessarily return the value you expect depending on the font since fonts are not necessarily upright and on teh otehr hand the bounding box around a character may be at a different angle than any straight edge in teh font. As a start you might consider the protractor tools to measure angles, but anything more specific than that will probably take you into geek territory...
Your question contains probably the easiest answer.
Draw a line or box, make it semi-transparent. Zoom in close & rotate the line positioning it over the letters - make a note of the angle.
This is probably the quickest, easiest way to get what you want.
Alternatively - if its a circle - you can rotate the circle until the letter your interested in is at the top 12 oclock position - how much did you rotate? then just cancel.