Make an hole at the center of a cylinder with a drill press
I'd create a channel out of wood blocks for the cylinder to lie in and pad it with a cloth. Something like this:



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Then I'd use an awl or nail set to create a divot in the surface of the acrylic. This will help prevent bit crawl, though a drill press usually takes care of that for you if you secure the work piece well. 

Acrylic melts easily, so either drill fairly quickly or use a fluid bath for cooling.