Circular dichroism, that is, the differential absorption of a system to left and right circularly polarized light, is one of the only techniques capable of providing morphological information of certain samples. In biology, for instance, circular dichroism spectroscopy is widely used to study the structure of proteins. More recently, it has also been used to characterize metamaterials and plasmonic structures. Typically, circular dichorism can only be observed in chiral objects. Here we present experimental results showing that a non-chiral sample such as a subwavelength circular nanoaperture can produce giant circular dichroism when a vortex beam is used to excite it. These measurements can be understood by studying the symmetries of the sample and the total angular momentum that vortex beams carry. Our results show that circular dichroism can provide a wealth of information about the sample when combined with the control of the total angular momentum of the input field.