Others have great answers on how to make the circle. I can recommend a bit I used in a router to cut straight lines in 1/4" acrylic for a showcase project for work.
From my notes I used an "Amana 51504" "slow spiral" bit. Solid carbide for 30$, but it worked like a charm. Beautiful edge like glass, no burrs. I never cut plexiglass, but after a couple trial cuts, really worked well. Speed/feed was important. Too fast and material can crack and too slow will melt the material. My records say I cut off a 48" sheet in 15 seconds, of course using a stiff straightedge.
Good Luck!