Ryan's advice works if you have something flat and round (i.e. not a dinner plate - you need it to have good large-area surface contact in order to safely stick it to the acrylic). Use double-sided carpet tape, available in the flooring section of HD/Lowes. After sticking the two together use a clamp to press around in various places to make sure you have a secure bond. It could be hazardous to your present 10-fingered-state if the pattern and stock were to separate during routing. After all that, carpet tape is more than sufficient for pattern routing.
A good way to make an initial pattern is to cut an acrylic square a quarter inch larger than the circle you want to make. drill a 3/8" or larger hole through the center of the acrylic square (the hole-center needs to be exactly the pattern radius away from one edge, and slightly farther from the other edges). Get a piece of plywood that you can clamp to the top of your router table. Drill a hole in it a little more than the pattern radius away from where the router bit will be. Push a 1" length of dowel into the hole. Mark where the edge of your circle will be on the board, and run the board into the router bit until you are just up to the line. Do it once more to widen the path for the bit. Turn off the router. Clamp the board in place on the router table. Put your square onto the dowel, turn on the router and turn the workpiece. You'll get a perfect square.
Now if you want different sized circles, just drill another hole in the plywood, and move the dowel to the appropriate radius distance from the router bit.