Normally in order to connect external hardware to your computer, you need a hardware interface or more commonly known as an I/O. These are varied in types and degree of ability. Unless your sound card is equipped with a set of input and output routing ports or you have some sort of hardware based I/O product, it will be difficult if not outright undoable simply by virtue of the need for input, and output connections.
Does your sound card have adequate input and output ports? Does your sound card have a software driver which offers a control panel of sorts enabling you to rout signal? That interface would be necessary so you can call upon the compressor from logic using an I/O soft patch in the utility menu?