The company also noted that it employed 443 Dreamers (DACA recipients) who "embody Apple's innovation strategy" by being some of the company's "most driven and selfless" staff. Moreover, it observed that immigration was central to Apple's story -- the late Steve Jobs was the son of a Syrian immigrant.

The company has filed amicus briefs before, but an Apple spokesperson confirmed to CNBC that this was the first time Cook had signed his name on one of them.

Courts aren't obliged to consider briefs like this when making decisions, but they can be influential if judges are receptive. And that's what Apple is hoping for. It's clearly betting that the judge will not only see DACA as a compassionate program, but that it makes economic sense by fostering motivated workers.