Without the aid of any measuring device, how can you use a transparent 16-ounce mug to measure a volume of water that is exactly 8 ounces?

Half the volume of a cylinder can be achieved by using the "diagonal".

The mug should be held such that the bottom of the open end is level with the top of the closed end. The amount it will hold in this position is 8 oz !

Can we assume the jug is a cylinder? Most jugs are wider at the top than the bottom.

Given that the VAST majority of mugs are cylindrical, and that the question does not specify otherwise, I think it's probably safe to make the assumption.

If the mug were NOT a conventional shape, it would surely have been mentioned in the question. It could be argued that Dark Bark's method would not work for irregular star-shaped mugs, but that is probably dividing the lifeless cells commonly found on people's heads.

Linus's reply re NOT being IRREGULAR is the key to this.
Providing both ends of the mug are the same shape AND the same size then it does not have to be a cylindrical mug.
However it MUST have SYMMETRY in all 3 dimensions.
To do this the STAR shaped mug would work but it would have to be a SIX (or 8,10,12 etc.) pointed star.
A five pointed star mug would not work.

Basically the mug has to have an EVEN number of sides.
The mug could be Square or Rectangular or even a RHOMBUS.
Hexagon and Octagon mugs would be fine, but a pentagon mug would not.

Hope I've made myself clear.