A router would work, you need to either drill a hole in a corner to put the router bit in to start or you need to have a plunge router so you can plunge the bit down through the material.
I will caution you about one thing, you will have to check to see if its true or not. I believe acrylic will tend to crack around any sharp inside corner so you need to make the inside corners rounded.
How big is the sheet you are cutting?
If its not too big you could do it on a table saw by dropping the blade all the way down, laying the sheet on the table saw with it where you want the cut and cranking the blade up through the sheet, then slide the sheet along to the end of the cut and drop the blade out.
that works well when you do not need rounded corners.
Also, a jigsaw will work but you need to make sure it has some sort of magic circle to keep it from chipping out the acrylic.
I think that is all I got for ya.
I am going to be cutting some similar holes in Makrolon (polycarbonate) next week, I am going to use a combination of tools. I am going to start by using a small circular saw and plunging it down through the sheet and cutting the straight bits with that, then a jig saw to cut the corners.
Hope that helps...
By the way, plunging a circular saw down is inherently dangerous, if you haven't done it before, practice on a piece of plywood until you have the technique down pat