There is no one-step method to align a non-rectangular workpiece on a laser cutter bed. When lots of similarly shaped objects are going to be engraved, a custom-cut jig is often employed to ensure that the alignment is consistent, but for a one-off job that can be overkill, and requires a fair amount of time to design and test the jig. All that is needed is a way to identify the center of object to be etched and line the laser up to that point. A piece of paper, some tape, and a pencil are all the tools required. I'll show you how I was able to etch the bottom of a shot glass, and you can apply the technique to your own project!
Step 1: Make a Rubbing of the Surface to Be Engraved
Get a blank piece of paper that is at least the size of the surface you are engraving. Having a larger piece of paper will help you get a more accurate center since your measurements can be more accurate.
Affix the paper to the surface to be engraved. I used single-sided tape stuck in a loop, but double-sided tape is less likely to move. Rubber cement would work fine too, I'm sure.
Using a graphite pencil, lightly rub around the edge of your object. This should transfer the outline of your object onto the paper. Use the side of the pencil when making the rubbing, not the tip, or you'll just poke holes in the paper.