I'm guessing that you are looking to do it in an inexpensive manner. Yes you can use a jigsaw to cut 3/16" acrylic. I do it regularly, but you need the correct blade. I use a 14 TPI metal cutting blade and I prefer the Lenox brand. However you need an edge guide to get a nice straight cut. Simply clamp a straight edge to the piece and cut along the guide going slowly. If it's a cheaper grade of plastic you may need to put some masking tape along the cut. It helps dissipate the heat from the blade because the plastic will sometimes melt back together. Do not use a wood blade because the teeth are too aggressive and will break the plastic.
A table saw with a plastic blade (as in the first response) is the "correct" way to go and will give the best cut.. My table 10" saw blade (a bigger blade will stay cooler) is probably 25+ years old but was not cheap, is 100 tooth and is a triple chip design, made especially for plastic. It also gives nice cuts on other materials, but isn't the best for thick wood. That blade mentioned above on Amazon is the correct type to use as well.